The American University in Cairo School of
Sciences and Engineering
Finite Element Dynamic Study on Large Framed
Foundation of Steam Turbine Generator
BY
Ahmed Mounir Ibrahim Abou Elsaoud
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Science in Construction Engineering
Under the supervision of:
Prof. Dr. Mohamed Abdel Mooty
Department of Construction and Architectural Engineering
The American University in Cairo
FALL 2011
ABSTRACT
The finite element modeling and dynamic analysis of massive and elevated foundation of
steam turbine generator is considered in this thesis. The element type, element size and
damping ratio are very important parameters in finite element modeling of massive machine
foundation in general and the steam turbine generator foundation in particular. Inefficient
modeling of the foundation may result in an unnecessary increase in the foundation size to
limit the vibration amplitude within the machine manufacturer specified limits. The work in
this thesis investigates the effect of damping ratio (2% to 5%), mesh size (500 mm, 800 mm
and 1100 mm), and element types (8-nodded element, 10-nodded element and 20-nodded
element) on the response of foundation to dynamic machine load as well as seismic loads.
First, a free vibration analysis is performed to accurately determine the natural frequencies
and to make sure that the effective modes of vibration are outside the critical frequency range
set by the manufacturer of the steam turbine generator. This is followed by harmonic analysis
to determine the foundation response to the machine load. Finally, the response of the
machine foundation to seismic forces is evaluated. Seismic analysis is performed using two
approaches: (1) by applying the seismic forces at the machine anchorage locations, (2) by
applying the seismic force at the center of gravity of the machine. Furthermore, concrete with
different compressive strength is considered to determine its effect on the critical harmonic
response of the structure to machine dynamic loads.
A detailed finite element model of the steam turbine generation foundation is constructed
using three dimensional solid elements model available in ANSYS finite element package.
This model is used to perform the free vibration and forced vibration analysis taking into
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consideration the above mentioned parameters. The influence of changes is those parameters
on the foundation response is determined. The results of the numerical dynamic analysis
performed on the machine foundation for free vibrations, harmonic forced vibrations, as well
as seismic response are reported and analyzed in this thesis.
Free vibration analysis showed that the change in the damping ratio has almost no effect on
the natural frequencies. Other parameters, however, slightly affect the free vibration
characteristics. For mesh sizes (500 mm to 1100 mm) the fundamental frequency values
increase by 1% to 2% for the 8 nodded elements and 0.4% to 0.6% for the 10 & 20 nodded
elements. Although the changes are not significant, it indicates that inaccuracy due to using
large size element can be overcome by using element with larger number of nodes. However,
since such changes are really small, element size of the order of 1000 mm for steam turbine
generator foundation of the size used in this study can be considered reasonable. Thus, less
complex finite element model can be used in such type of analysis without adversely
affecting the accuracy of the results.
Forced vibration response of the massive machine foundation is considered through
evaluating its steady state harmonic response which is found to be more sensitive to changes
in the studied parameters than the free vibrations. The transverse and vertical response values
of the foundation at the turbine supporting points are affected by the change in damping ratio,
mesh size, and element type. For the same mesh size and element type, the increase in the
damping ratios from 2% to 5% results in decreasing the horizontal displacement by a range
from 10% to 15% while the vertical displacement decreases by a bigger range from 16% to
32%. Also for the damping ratios (2% to 5%) and mesh sizes (500 mm to 1100 mm) the
iii
vertical and horizontal displacements have the same values for the 10-nodded and 20-nodded
elements which are 2% to 20% higher than the values of the 8-nodded elements. Therefore,
the use of 10-noded element is recommended for forced vibration analysis of machine
foundation of the size used in this study. It is concluded that the damping ratio has significant
effect on the structural response in the harmonic analysis of the foundation. The difference in
response due to the changes in the compressive strength is found to be minor and this can be
justified by the fact that the foundation overall dimensions and the member sizes are kept
unchanged.
The displacement resulting from applying seismic force at the machine sole plates is
approximately 2% more than the deflection resulting from applying seismic force at the
center of gravity of the machine. This is due to the small distance between the foundation
tabletop and the machine as the center of gravity of the machine is located 900 mm above the
foundation elevation.
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Table of Content
Abstract
ii
Table of Content
iv
List of Figures
vii
List of Tables
ix
Chapter 1
Introduction
1
1.1
Objective and scope of work
2
1.2
Literature Review
3
1.3
Machinery Types
10
1.3.1
Reciprocating machinery
10
1.3.2
Impulsive machinery
11
1.3.3
Rotating Machinery
12
1.4
1.5
Types of turbine generator foundations
13
1.4.1
Block foundations
13
1.4.2
Frame foundations
15
Vibrating systems
19
1.5.1
Free vibration for a SDOF vibrating system
19
1.5.1.1
Free un-damped vibration of SDOF vibrating system
20
1.5.1.2
Free damped vibration of SDOF vibrating system
21
1.5.2
Harmonic vibration for a SDOF vibrating system
22
Chapter 2
Turbine Generator Machines
24
2.1
Brief description of turbine generator machine
24
2.1.1
Low tuned foundation
26
2.1.2
Conventional foundation
v
26
2.1.3
2.2
High tuned foundation
26
Loads acting on turbine generator foundation
27
2.2.1
27
Dead load
2.2.1.1
Foundation dead load
27
2.2.1.2
Machine dead load
28
2.2.2
Live load
28
2.2.3
Condenser load
28
2.2.3.1
Condenser dead load
30
2.2.3.2
Condenser vacuum load
30
2.2.4
Normal torque load
31
2.2.5
Thermal Loading
32
2.2.5.1
Machine expansion contraction
32
2.2.5.2
Thermal gradient in foundation due to operation
32
2.2.6
Normal machine unbalanced loads
33
2.2.6.1
33
Dynamic Forcing Function
2.2.7
Generator Emergency Torque
36
2.2.8
Load due to out of phase synchronization
37
2.2.9
Load due to bowed rotor
38
2.2.10
Load due to missing rotor blade
40
2.3
Response to dynamic load of operation
42
Chapter 3
The Steam Turbine Generator Pedestal (Case Study)
44
3.1
Introduction
44
3.2
Structural Description
45
vi
3.3
Site Condition and Soil Properties
52
3.3.1 Static and Dynamic Stiffness Determination
54
3.3.1.1 Axial Pile Springs
54
3.3.1.2 Lateral Pile Springs
55
3.4
Finite element 3D model
3.4.1
56
SOLID 45 [8-nodded element]
57
3.4.2
SOLID 92 [10-nodded element]
57
3.4.3
SOLID 95 [20-noded element]
58
3.4.4
Combin14 [spring-damper element]
60
3.5
Scope of Analysis in the current study
64
Chapter 4
Analysis of Results
67
5.1
4.2
Modal Analysis
67
4.1.1
80
Modal analysis results summary
Harmonic Analysis
81
4.2.1
91
Harmonic analysis results summary
4.3
Seismic Analysis
93
4.4
High Strength Concrete
96
Chapter 5
Summary and Conclusion
97
5.1
Summary
97
5.2
Conclusion
98
vi
i
LIST OF FIGURES
1.1
Compressors
10
1.2
Diesel Engine
11
1.3
Forging Hammer
11
1.4
Combustion Turbine Generator Machine
12
1.5
Steam Turbine Generator Machine
13
1.6
Block type foundation
14
1.7
Block foundation resting on soil
14
1.8
Block foundation resting on piles
15
1.9
Frame foundation
16
1.10
Longitudinal profile of a steam turbine generator foundation
17
1.11
Typical cross section of steam turbine generator foundation and the powerhouse
18
1.12
Idealized structure representing the free vibration (SDOF) vibrating system
20
1.13 Free vibration of a system without damping with natural period of vibration
20
1.14 Idealized one story structure for a damped SDOF system
21
1.15
Response of damped SDOF system with
21
1.16
Harmonically excited damped system
22
1.17
Response Factor for a System Subjected harmonic force
23
2.1
Steam Turbine Generator Machine Components
24
2.2
Directions of the Applied Forces on Turbine Generator Foundation
27
2.3a
Condenser is rigidly supported
30
2.3b
Condenser is mounted on springs
31
2.4
Torque load due to machine rotation
33
2.5
Rotating eccentric mass
34
2.6
unbalanced forces along shaft with multiple supports
vi
ii
35
2.7
Load due to missing rotor blade
41
3.1
Isometric view of the STG machine foundation system
46
3.2
Plan view of the STG machine foundation system at top surface of the base mat
47
3.3 Plan view of the STG machine foundation system at tabletop elevation
48
3.4
Elevation view at section A-A
49
3.5
Elevation view at section D-D
50
3.6
Plan view of pile arrangement
51
3.8
Solid 45 (3D Structural Solid)
57
3.9
Solid 92 (3D Structural Solid)
58
3.10 Solid 95 (3D Structural Solid)
59
3.11 Combin14 (spring-damper)
60
3.12 Finite element model
61
3.13
62
Rigid region location
3.14 Rigid Links & Machine Bearing Locations
63
3.15
The bearings connected to the table top through the rigid links
64
4.1
First mode shape, 2% damping, mesh size 500mm & 8-nodded element
75
4.2
Second mode shape, 2% damping, mesh size 500mm & 8-nodded element
76
4.3
Third mode shape, 2% damping, mesh size 500mm & 8-nodded element
77
4.4
Fourth mode shape, 2% damping, mesh size 500mm & 8-nodded element
78
4.5
Fifth mode shape, 2% damping, mesh size 500mm & 8-nodded element
79
4.6
Sectional Elevation Showing the Locations of Bearings
82
4.7
Response to harmonic analysis in horizontal direction (1)
85
4.8
Response to harmonic analysis in vertical direction (1)
86
4.9
Response to harmonic analysis in horizontal direction (2)
87
4.10
Response to harmonic analysis in vertical direction (2)
ix
88
4.11
Response to harmonic analysis in horizontal direction (3)
89
4.12
Response to harmonic analysis in vertical direction (3)
90
4.13
The Deflection due to seismic applied on sole plates
94
4.14
The Deflection due to seismic applied on machine CG at rigid links
95
LIST OF TABLES
3.1
Dynamic and Static stiffness
53
3.2
Summary of soil properties at the STG foundation area
54
4.1
Frequency corresponding to mode shapes (1)
68
4.2
Mass corresponding to frequency (1)
69
4.3
Frequency corresponding to mode shapes (2)
70
4.4
Mass corresponding to frequency (2)
71
4.5
Frequency corresponding to mode shapes (3)
72
4.6
Mass corresponding to frequency (3)
73
4.7
Modal Analysis Results Summary
81
4.8
Dynamic unbalanced loads
82
4.9
Harmonic Analysis Results Summary
92
4.10
Seismic Analysis Response Results Summary (Seismic)
93
4.11
Seismic Analysis Response Results Summary (High strength)
96
x
Chapter 1
Introduction
Turbine generator machines form the heart of any power plant. Thus for any developed or
developing nation, capacity of supplying unhindered energy not only ensures a steady
industrial growth, but also goes into improve the quality of life in long way. The main
source of this energy is obviously electricity and this is what the turbine generators
machines generate. The turbine generator machine is one of the most important and
complicated system in design, manufacturing and testing. The turbine generator machine
has a huge weight usually ranging from 6000 kN to 17000 kN, which is imposed on a
large massive concrete foundation pedestal. Thus if the foundation which supports these
critical machines misbehave and the machine trips during operation, the consequences on
the end user and the industry dependent on the power generated could suffer severe
losses. If the shortage is severe in nature, this could even have a very adverse effect on
the economic growth to a complete part of a country. Accordingly, we can say that for
successful operation two aspects become critical for these machines : 1) The machine
itself should run smoothly (round the clock) ; 2) The foundation supporting the
equipment is capable of sustaining the various loads coming from the turbine under
operation (dynamic loads) as well as those that could develop due to the vagaries in
nature or otherwise like earthquake, thermal, electrical faults, short circuits etc.
The structural engineer plays an important role in the analysis and design of such
foundations and structures subjected to dynamic loads especially for the turbine
foundation. The analysis is considered a very complex problem because of the interaction
of the structure, the subsurface soil, and the vibrating machine. The analysis and design
of these foundations and structures became less complex after the introduction of the
1
finite element method and digital computer. The concern of this study is the machine
foundation in general and the large framed turbine foundation in specific. Such
foundation type is subjected to time and frequency varying loads due to the machine
oscillations. Under such types of loading a full dynamic analysis should be considered
where the machine operation would affect either the entire structure or certain
components of that structure. The effect of foundation on these vibrations during the
machine operation is severe and the application of the dynamic principles in evaluating
the response of the structure is very important.
Normally the dynamic analysis using any finite element method is carried out using a
deterministic approach with constant material properties, damping ratios, element type. In
this thesis, the effect of those governing parameters that affect the global response of the
foundation is studied. In addition, the response of the turbine generator foundation to
seismic loads using two approaches in applying the machine load to the foundation is also
studied.
1.1 Objective and scope of work:
The objective of this study is to determine the dynamic response of the turbine foundation
where the effect of different parameters on the calculated response is evaluated. This
includes:
a) Damping ratios, a range of damping ratios is considered. The analysis
starts with 2% to 5% damping ratios with 1% increase in the damping
ratio.
b) Element type, the effect of using different solid element types with 8, 10
& 20 nodded element.
2
c) Element size, the effect of using different element (mesh) sizes 500 mm,
800 mm & 1100 mm.
d) Concrete compressive strength, the effect of using concrete with different
compressive strength (32 MPa, 50 MPa and 75 MPa).
The effect of these parameters change on the foundation natural frequency is calculated
and the dynamic response is calculated under the effect of harmonic steady state
excitation. Moreover, the change in the type and size of the solid elements used in the
finite element will affect the time and cost of computation, for example the analysis
performed using solid element 20 nodded with and 500 mm mesh size takes about 48
hours.
In addition, evaluation of foundation response to seismic effect is studied. Two different
models for machine mass location are considered. First one by applying the seismic force
at the machine anchorage locations, and the second model by applying the seismic force
at the center of gravity of the machine.
1.2 Literature Review
The dynamic analysis of structures is usually performed through the selection of an
idealized model consisting of springs with adequate stiffness to capture the actual
stiffness of the structures, the masses and the damping elements. Many techniques are
adapted to model structures subjected to dynamic loading. The use of finite element
techniques and digital computers in the analysis of space structures during the 1960’s
and in modelling structures for nuclear and fossil power generation plants has led to a
significant progress in the area of structural dynamics. Many modelling techniques have
been proposed to model structures subjected to dynamic loading. Some of these
3
techniques adopt mathematical solutions and other models adopt the use of finite element
method. Many researchers have followed the concept of mathematical models to represent
the dynamic response of a physical problem of machine foundations under the effect of
dynamic loading. On this context some researches can be highlighted as follows:
1 – V. Karthigeyan, G.K.V. Prakhya and K. Vekaria, 2001 (ref. 17). The authors have
presented a finite element model for a steam turbine tabletop using a combination of
beam and plate elements. More importantly they have illustrated how connectivity
conditions of the shafts to casing and casing to concrete table and complex configurations
can be modeled in order that the loads are applied correctly with due regard for load paths
to the table. The modeling also allowed for accurate location of center of gravity and
realistic mass moment of inertia of the machine components such as turbine casing, rotor,
alternator stator, rotor, and condenser.
It was observed that harmonic analysis was carried out to compute the amplitudes of
vibration for the out-of-balance machine loads and to limit them to a suitable acceptance
criterion. The study highlighted that the amplitudes computed from the detailed finite
element model are higher than that computed from lumped mass models due to the
participation of flexural modes.
2 –Ali Ossama, 2006 (ref.3). The comparative study between the two models (frame
element and brick element models) was performed under the effect of time domain
dynamic forces (steady state forces), and frequency domain dynamic forces (harmonic
excitation forces). Two numerical models were constructed to study the effect of
element type and rigid links distribution on the mass foundation pedestal responses. In
the first model, beam elements were used to model the operating floor longitudinal
4
and transverse floor mass beams, while in the second model, three dimensional
isoparametric brick elements were used to model the same foundation pedestal. The
masses of the turbine machine were lumped at the model joints. The two models were
excited dynamically with harmonic excitation forces and steady state excitation forces.
The response of the two numerical models due to the dynamic excitation forces was
compared. The mass participating ratios of the foundation global modes of vibration
and the natural frequencies are affected by the element type and rigid links distribution.
In the lateral direction, the percentage of the masses acting in the lateral direction for
the brick model using isoparametric elements is higher by 34 % than the masses acting
in the lateral direction using the prismatic beam elements. In the vertical
direction, the masses participating in the brick model was found to be higher by 42
% than the beam model. Under harmonic excitation, the amplitude of beam model
response was higher by a range of 10% to 72% in the lateral direction than the brick
model and by 100 % in the vertical direction, i.e. the vibration amplitude under
harmonic excitation of the beam model is twice the amplitude captured by using
brick elements as the modeling block for the foundation. Under steady state
machine operation, the same trend of response was observed. The brick model
response showed 50% higher rigidity than that of the beam model.
3 – Gu Ping, 2009 (ref.13). This paper proposes a new dynamic participation factor
(DPF) for analysis and design of structures supporting rotational machines, especially
large turbine generators. The new DPF takes into account the distribution patterns of the
machine unbalanced forces and addresses the phase lags among the forces at different
bearings and between the different force components. An example of a real turbinegenerator foundation is presented and the new and traditional DPFs are compared along
5
with examination of the vibration modes. The results show that the new DPF can clearly
identify the local vibration modes that cause severe resonance. Using the traditional DPF
could cause engineers to ignore these modes and, consequently, result in unsafe design.
The common misconceptions of dominant fundamental modes and low tuning are
clarified. Harmonic analyses (frequency sweeps) are also performed and the results are
compared with the results of the new DPF analyses. The new DPF analysis has clear
advantages over the harmonic analysis in that it provides a complete picture of the
dynamic behavior of the whole structure and does not need the engineer to anticipate the
local vibration points. The new DPF analysis can also be used to guide the selection of
locations for vibration amplitude check and provides an alternative method to consider
the different phasing of bearing loadings, which produces responses to real loading cases.
4 – Lakshmanan N., 2006 (ref.16). Turbo generator pedestals are one of the critical
structures in any power plant complex. Stringent vibration requirements particularly at
the bearing locations have been stipulated for proper functioning of turbo generator
installations. Normally the dynamic analysis is carried out using a deterministic approach
with constant material properties. The effect of variability of modulus of elasticity of
concrete, and operating speed of the turbo generator can lead to increased amplitudes of
vibration. The designer always looks for conservative estimates of the expected responses
and is interested in keeping them within allowable limits. This paper provides a
methodology for computing peak dynamic response at bearing locations once the results
of the dynamic analysis with a given input stiffness is available. The approach is
essentially based on modal synthesis of responses, namely contribution of individual
modes to amplitude of vibration at a particular location. The frequency range of interest
is divided into three regions, namely, nonresonant region where undertuned conditions
6
exist, nonresonant region where overtuned conditions exist, and the resonant region.
Simple analytical formulation has been developed to compute the peak dynamic response
and is illustrated with an example. The suggested method can be programmed for
effective use through spread sheet.
5 - Sienkiewicz Z. & Wilczyński B., 1993 (ref. 26). In this paper, a numerical model for
the minimum‐ weight design of a rectangular machine foundation under a harmonic
vertical load is presented. The analysis of the dynamics of foundation‐ soil interaction
is based on frequency‐ dependent dynamic properties of a semi‐ infinite supporting
medium and includes the shape of the foundation plan, the embedment of the foundation
into the soil, and hysteretic material damping of the soil. Dimensions of the concrete
block are assumed as design variables. Constraints are placed on resonant frequency,
vertical displacement amplitude, stresses in the soil and dimensions of the foundation
concrete block. A sequential programming method with variable move limits is used to
obtain the optimal solution, which is affected by inertia properties of the Machine ‐
foundation ‐ soil system, damping from dynamic soil‐ foundation interaction and local
soil conditions. Numerical examples are given to demonstrate the applications of the
proposed approach.
6 - Gazetas George, 1982 (ref. 13). The paper reviews the state-of-the-art of analysing the
dynamic response of foundations subjected to machine-type loadings. Following a brief
outline of the historical developments in the field, the concepts associated with the
definition, physical interpretation and use of the dynamic impedance functions of
foundations are elucidated and the available analytical/numerical methods for their
7
evaluation are discussed. Groups of crucial dimensionless problem parameters related to
the soil profile and the foundation geometry are identified and their effects on the
response are studied. Results are presented in the form of simple formulae and
dimensionless graphs for both the static and dynamic parts of impedances, pertaining to
surface and embedded foundations having circular, strip, rectangular or arbitrary plan
shape and supported by three types of idealized soil profiles: the halfspace, the stratumover-bedrock and the layer-over-halfspace. Consideration is given to the effects of
inhomogeneity, anisotropy and non-linearity of soil. The various results are synthesized
in a case study referring to the response of two rigid massive foundations, and practical
recommendations are made on how to inexpensively predict the response of foundations
supported by actual soil deposits.
7 - Hadjian H. Asadour, 1970 (ref. 15). American design practices and criteria for large
turbine generator pedestals are reviewed. Parametric studies show that, irrespective of its
rigidity, the mat should be included as part of the pedestal for both dynamic and static
analyses. It is argued that differential rather than absolute deflections are more
meaningful design constraints. Arbitrary specification of dynamic loads should be
discontinued since dynamic loads are a function of both the forcing property and the
dynamic characteristics of the structure. Temperature, shrinkage and creep, especially as
they affect large sized members, need to be given further consideration. To attain the
required accuracy in deflection calculations, torsional and bending stiffnesses of
reinforced concrete pedestals must be better defined. Examples are given t illustrate that
the design of large-size reinforced concrete members for flexure, torsion and shear cannot
be extrapolated from findings n the laboratory sized specimens.
8
The types of machinery that are supported on the machine foundation are presented in the
next section 1.3. Heavy machinery with reciprocating, impacting, or rotating masses
requires a support system that can resist dynamic forces and the resulting vibrations.
When excessive, such vibrations may be determinable to the machinery, its support
system, and any operating personnel subjected to them.
8 - Lui, W. and Novak, M., 2006 (ref. 20). In this paper a comprehensive investigation on
the dynamic characteristics of turbine–generator–foundation systems is performed. All
the major components of the system, including turbine–generator casing, shaft, rotors,
journal bearings, deck, piers, foundation mat, piles, and soil medium, have been included.
Full interaction between the turbine–generator set, the foundation superstructure, and the
soil medium, is considered.
A hybrid method is used to establish the mathematical model for the turbine–generatorfoundation system. The analysis is conducted in the frequency domain through complex
frequency response analysis. The response in the time domain is obtained by Fourier
transform. The seismic excitation is represented as the control motion on the ground
surface, which is generated as an artificial earthquake.
A 300 MW turbine-generator-foundation system is analysed under excitations from rotor
unbalances and earthquakes. The influence of turbine-generator casing and soil
anisotropy on the response of the system is explored. It is found that the presence of
casing and soil anisotropy strongly influences the displacements and internal forces of the
system under rotor unbalance excitation. Under seismic excitation, however, although the
presence of casing and soil anisotropy does affect the displacements of the system, their
effect on the internal forces of the system is minimal.
9
1.3 Machinery types:
1.3.1 Reciprocating machinery: This category includes machines such as compressors
(Fig. 1.1) and diesel engines. The mechanism of motion for such machines is a piston
moving in a cylinder interacts with a fluid through the kinematics of slider crank
mechanism driven by or driving, a rotating crankshaft.
Figure 1.1 Compressors (http://www.maritimejournal.com)
10
Figure 1.2 Diesel Engine (http://www.magnate-ventures.com)
1.3.2 Impulsive machinery: Equipment, such as forging hammers and some metalforming presses, operate with regulated impacts or shocks between different parts of the
equipment. This shock loading is often transmitted to the foundation system of the
equipment and is a factor in the design of foundation.
Figure 1.3 Forging Hammer (http://www.bridgat.com)
11
1.3.3 Rotating machinery: This category includes gas and steam turbines, turbo-pumps,
compressors and fans. The rotating motion of the rotors characterizes these machines.
Unbalanced forces in rotating machines are created when the center of mass of the
rotating part does not coincide with the center of rotation. This dynamic force is a
function of the shaft mass, speed of rotation, and the magnitude of the offset. The offset
should be minor under manufactured conditions when the machine is well balanced,
clean and without wear or erosion. Changes in alignment, operation near resonance, blade
loss, and other malfunctions or undesirable conditions can greatly increase the force
applied to its bearings by the rotor. Because rotating machines normally trip and shut
down at some vibration limit, a realistic continuous dynamic load on the foundation is
that resulting from the vibration just below the trip level. Our concern here from the
above mentioned machinery types is the rotating machinery represented by the turbine
generator machine.
Figure 1.4 Combustion Turbine Generator Machine (http://archive.powerauthority.on.ca)
12
Figure 1.5 Steam Turbine Generator Machine (http://allaboutmagnets.wikispaces.com)
1.4 Types of turbine generator foundations
There are different types of foundations used to support the turbine generator machines
and it can be classified into two main types: Block foundations and frame foundations.
1.4.1 Block foundations.
Dynamic machines are preferably located close to grade to minimize the elevation
difference between the machine dynamic forces and the center of gravity of the machine
foundation system (Fig. 1.6). The ability to use such a foundation primarily depends on
the quality of near surface soils. Block foundation are nearly always designed as rigid
13
structures. The dynamic response of a rigid block foundation depends only on the
dynamic load, foundation’s mass, dimensions, and soil characteristics.
Figure 1.6 Block type foundation. (Ref. 9)
This type of foundation usually consists of massive reinforced concrete block rested on
soil or on piles as shown on (Fig. 1.7 & 1.8)
Figure 1.7 Block foundation resting on soil. (Ref. 9)
14
Figure 1.8 Block foundation resting on piles. (Ref. 9)
Block type foundation are usually used to support combustion (gas) turbine generators
machines, also this type of foundation is used to support other machines such as pumps,
motors, coal mill foundations, motor driven boiler feed pumps, centrifugal / reciprocating
type compressors and generators
1.4.2 Frame foundations.
Elevated support is common for large turbine-driven equipment. Elevation allows for
ducts, piping, condenser(s) and ancillary items to be located below the equipment. Frame
foundations are considered to be flexible, hence their response to dynamic loads can be
quite complex and depend both on the motion of its discreet elements (columns, beams,
and footing) and the soil upon which it is supported. Steam turbine generator machines
are usually supported on this type of foundation. The other types of equipment supported
15
on these types of foundations like boiler feed pumps in power plants, compressors in
petroleum refineries and air blowers in automobile industry. This type of foundation
usually consists of reinforced concrete base mat with columns or walls supporting the
tabletop (operating deck) (Fig. 1.9).
The operating deck is elevated to provide for installation of condenser(s) directly under
the turbines (Fig. 1.10). This reinforced concrete foundation rests on soil or on piles.
Figure 1.9 Frame foundation. (Ref. 9)
16
Figure 1.10 Longitudinal profile of a steam turbine generator foundation. (Ref. 9)
Steam turbine generator foundations are usually placed in a powerhouse, in other words
steam turbine generator building. Figure 1.11 shows a cross section for the steam turbine
generator foundation and the powerhouse.
17
Figure 1.11 Typical cross section of steam turbine generator foundation and the
powerhouse. (Ref. 9)
The discussion here will be restricted to the steam turbine generator machines in power
plants. The quality and performance of the machines are controllable since materials used
are all man made and all requisite parts are manufactured under careful controlled
condition. However, for civil engineer designing its foundation the situation is
completely different. The designer neither has control on the subsoil on which it is being
built nor he has any control on the natural forces like earthquake load on such large mass
18
system. In addition to this the number of uncertain loads that should be defined at the
start of the design like piping loads, stator loads, and electrical fault loads need to be
considered in the design of such machine foundation.
Usually for a normal foundation, static load predominates. While for machine foundation,
it is just the reverse. In most of the industrial facilities, production being round the clock,
the major load acting on the foundation is dynamic in nature and the foundation should
be capable to sustain this dynamic loads in addition to the static loads and this should be
performed without any distress to the underlying soil or to the machine it is supporting.
1.5 Vibrating system.
Turbine generator pedestals are one of the critical structures in any power plant complex.
Stringent vibration requirements particularly at the bearing locations are stipulated for
proper functioning of turbo generator installations.
Vibration is time dependant, repeating motion of translational or rotational type of any
body possessing mass and elasticity. Vibration due to machine operation is classified as
free vibration or harmonic (forced) vibration. Components and types of single degree of
freedom (SDOF) vibrating system will be breifly discussed as follows.
1.5.1 Free vibration for a SDOF vibrating system.
Free vibration takes place when a structure vibrates under action of forces inherent in the
system itself (mass and restoring stiffness) and in the absence of external force or ground
motion. The study of free vibration leads to the determination of the natural vibrating
frequency and damping ratio for a SDOF system. The rate at which the motion decays in
free vibration is controlled by the damping ratio.
19
1.5.1.1 Free un-damped vibration of SDOF vibrating system.
Figure 1.13 represents the behavior of the system at figure 1.12 undergoes free undamped vibration, the mass (M) should be displaced laterally with initial displacement
(Uo) as shown in (Fig 1.8), then released and permitted to oscillate freely around its
initial equilibrium position. Theoretically, these oscillations will continue forever with
the same amplitude (Uo) and the structure would never come to rest and this can be
represented in (Fig 1.13)
Figure 1.12 Idealized one story structure representing the un-damped free
vibration (SDOF) vibrating system. (Ref. 8)
Figure 1.13 Free vibration of a system without damping due to initial displacement Uo (Ref. 8)
20
1.5.1.2 Free damped vibration of SDOF vibrating system.
In order to incorporate the damping feature in the dynamics of the structure, an energyabsorbing element known as viscous damper is introduced to the vibrating system (Fig
1.14), Figure 1.15 represents the behavior of the system at figure 1.14 undergoes free
damped vibration, the damping force is assumed to be proportional to the mass velocity
and always opposes the motion of the mass in a continuous linear function results in the
movement decay for the system.
Figure 1.14 Idealized one story structure for a damped SDOF system. (Ref. 8)
Figure 1.15 Response of damped SDOF system (Ref. 8)
21
1.5.2 Harmonic vibration for a SDOF vibrating system.
The concern of this thesis is the response of turbine generator foundation subjected to
harmonic forcing function of time due to the dynamic action of rotation. This harmonic
excitation is due to the unavoidable presence of mass eccentricities in the rotating parts of
the turbine generator machines. These mass eccentricities produce unbalanced forces that
induce continuous vibrations on the supporting structure during the machine operation.
These vibrations magnitudes represented by a sine or cosine functions of time. The
turbine generator machines are supported on concrete or steel structures. This system
considered as a vibrating system under the influence of viscous damping. (Fig. 1.16)
Represents the mechanical model for the turbine generator foundation vibrating system.
Figure 1.16 Harmonically excited damped system (Ref. 8)
1.5.2.1 Dynamic Magnification Factor
The dynamic magnification factor or the response factor as shown at fig. 1.17 varies with
the frequency ratio β and the damping ratio ξ. Fig. 1.17 shows a plot for the dynamic
magnification factor versus the frequency ratio for damping ratios from 0 to 1. It is
observed from the plot fig. 1.17 that for lightly damped systems the peak amplitude
occurs at a frequency ratio very close to β = 1; that is, the dynamic magnification factor
22
has its maximum value at resonance i.e. β = 1. it can also seen from the same plot that at
resonance the dynamic magnification factor is inversely proportional to the damping
ratio.
Figure 1.17 Response factor for a system subjected to harmonic force. (Ref. 8)
23
Chapter 2
Turbine Generator machines
2.1 Brief description to turbine generator machines
The main components of the turbine generator machines are the high and low-pressure
turbine sections, generator, exciter, and condenser.
Figure 2.1 Steam Turbine Generator Machine Components. (Ref. 9)
Turbines are classified as tandem compound or cross compound units. In tandem
compound units, one or more turbine sections are connected along a single shaft to the
generator. In cross compound units, high and low pressure sections are mounted on
separate shafts, with an independent generator for each shaft. In most cases, each shaft
rotates at a different speed.
A turbine section may be classified as single flow, double flow, or opposed flow. In a
single flow section, the steam expands along a single axial direction. A double flow
24
section contains two symmetrical steam paths; steam enters the center of the section and
expands in opposite axial directions. An opposed flow section is similar to a double flow
in that the steam expands in opposite axial directions, however the staging is not
symmetrical.
Turbine generator shafts are supported on bearings between turbine sections. Some
designs use two bearings per rotor, one at each end, while other designs use a single
bearing between turbine sections. On some machines the bearings are supported within
the turbine generator casing. On other machines, the bearings are supported on the
transverse beams independent of the casings. Each shaft is carefully aligned and balanced
to ensure low vibration operation. Misalignment of the shafts may result in serious
vibration problems and the initiation of cracks in couplings and other rotating parts.
The low pressure turbine exhaust nozzle is connected to the condenser. The function of
the condenser is to condense the turbine exhaust steam, which is then returned to the
steam supplied system in the form of condensate. A vacuum is formed inside the
condensers due to the volume reduction occurring as the steam changes from the vapor to
the liquid state. Condensers are cooled by circulating water, which passes through the
condenser shell in thin wall tubes to enhance heat transfer without contacting or mixing
with the condensate.
The turbine(s) and generator are mounted on manufacturer supplied sole plates, which are
grouted and bolted to the foundation in accordance to the manufacturer’s specifications.
The turbine generator is designed to slide on these sole plates to relieve stress due to
thermal expansion and contraction. Transverse and axial guides or keys are provided to
prevent misalignment to the shaft due to this thermal movement.
25
On most turbine generator machines, a system that measures the magnitude of the shaft
vibrations is installed. Trip limits are established for each machine. If any of the shaft
vibrations exceed this value, the unit will trip to prevent the damage of the machine.
Generally, the value of the limiting absolute rotor displacement is about 30 microns peak
to peak.
Generally, the concrete foundation pedestals classifications are based on the relative
natural frequency of the foundation pedestal with respect to the machine operating speed.
Based on this, the foundation pedestal can be grouped in three main groups: Low tuned
foundation, conventional foundation and high tuned foundation.
2.1.1 Low tuned machine foundation.
This type of foundation has a fundamental frequency much lower than the running speed
of the machine and is characterized by extremely slender columns. In this type, the ratio
of machine steady state operating frequency to the fundamental natural frequency is
greater than 3.
2.1.2 Conventional machine foundation.
In this type, the ratio of machine steady state operating frequency to the fundamental
natural frequency is greater than 1.4 and less than 3.
2.1.3 High tuned machine foundation.
This type is extremely massive and stiff. The ratio of machine steady state operating
frequency to the fundamental natural frequency is less than 0.7.
26
2.2 Loads acting on turbine generator foundation.
The turbine generator foundation must be designed to withstand all the forces that may be
imposed on it during the service life of the plant. The directions of the forces applied on
the turbine foundation are shown in Fig. 2.2. Actual loading on the turbine foundation
may vary from machine to machine. However, the type of loads acting on the turbine
foundation may generally be defined as shown in the following subsections.
Figure 2.2. Directions of the Applied Forces on Turbine Generator Foundation
2.2.1 Dead load.
2.2.1.1 Foundation dead load (DF)
The foundation dead load includes the self-weight of all members of the foundation.
27
2.2.1.2 Machine dead load (DM)
The weight of the turbine generator machine is considered the machine dead load.
2.2.2 Live load (LL)
The live load includes the load that varies in intensity and/or occurrence. The live load
from floor slabs supported by the turbine foundation should be a minimum of 10 KN/m2
or as required by any code requirement. Maintenance loads, such as lay down loads are
also considered a live load.
2.2.3 Condenser load (CL)
The type of connection between the turbine and condenser and the method of supporting
the condenser at its base determine the manner in which the condenser load is transmitted
to the foundation. Figures 2.3a and 2.3b show two common methods of supporting the
condenser. In the first method (fig. 2.3a), the bottom of the condenser is mounted on rigid
supports and an expansion point is placed between the condenser and the turbine exhaust
nozzle to relieve thermal forces and variations in the condenser load. Alternatively,
(fig. 2.3b), the bottom of the condenser is mounted on springs, while the top is connected
rigidly to the turbine exhaust nozzle. The springs can be adjusted to transfer specified
maximum and minimum loads to the turbine exhaust nozzle. They can also be adjusted to
compensate for load eccentricity, such as those from the circulating water pressure load.
28
Figure 2.3a. Condenser is rigidly supported and an expansion joint is placed between
condenser and turbine exhaust nozzle. (Ref.1)
Figure 2.3b. Condenser is mounted on springs that are adjusted to transfer as specified
minimum/maximum force. (Ref. 1)
29
2.2.3.1 Condenser dead load (CD)
When the bottom of the condenser is mounted on rigid supports, the entire dead weight of
the condenser is transmitted to the mat of the turbine foundation. While, when the
condenser is welded to the exhaust nozzle and supported on springs, the proportion of the
condenser load distributed between the deck level and the mat level depends on the
stiffness and initial settings of the springs supporting the condenser.
2.2.3.2 Condenser vacuum load (CV)
When an expansion joint is provided between the condenser and the turbine exhaust
nozzle, the difference between the atmospheric pressure on the casing of the turbine and
the vacuum pressure between inside the condenser results in a force on the turbine. This
vacuum load can be as large as several times the weight of the condenser. The direction
of the vacuum force is vertical acting in two opposite direction, downward at the
operation deck at the low-pressure turbine location and upward at the condenser piers at
the condenser location. Typically, one condenser unit is provided for each low-pressure
turbine, and its vacuum load is transmitted to the foundation through the turbine sole
plates at the operating deck (acting downward) and the condenser sole plates at the base
mat (acting upward). The soil or the piles under the foundation is not affected by this load
because the net force of the condenser vacuum load on the whole foundation is zero, so it
is used only in the strength design for the structural elements: operating deck beams,
columns and base mat.
30
2.2.4 Normal torque load (Wr)
The steam forces in each turbine section impose a torque on the stationary casing in the
opposite direction from the rotation of the rotor. This type of torque load results from the
magnetic coupling between the machine rotor and stator, which generate an overturning
torque oriented about the turbine generator axis. For the turbine and generator, this is
known as normal operational torque. This torque is oriented in the directions of the rotor
rotation and applied at the machine bearing supports as pair of vertical couples. The
magnitude of the torque depends on the rotational speed and the power output of the
turbine section. The turbine manufacturer tabulates specific torque loads on the
mechanical outline drawing as equivalent vertical loads on the soleplates. (Fig. 2.4)
Figure 2.4 Torque load due to machine rotation (Ref. 13)
31
2.2.5 Thermal loading
2.2.5.1 Machine expansion and contraction (TM)
Changing temperatures of the turbine and generator cause expansion and contraction
forcing the various parts to slide. As the machine heats up, the entire shaft expands.
However, it does not impart any loading on the foundation since the entire shaft system is
fixed longitudinally by a single thrust bearing, and the shaft slides freely across the welllubricated journal bearing. Unlike the expansion of the shaft, it is the heat buildup in the
casing that imposes the thermal loading on the foundation during the thermal transient.
The casing expands from the anchor points, thus producing the frictional loads. These
thermal loads do not impose a net resultant force on the foundation, since the forces on
any soleplate are balanced by equal and opposite forces on the anchors or on other
soleplates.
2.2.5.2 Thermal gradient in foundation due to operation (TF)
The stresses and deflections due to thermal expansion of the foundation due to any
environmental effects should be considered in design. Applicable situations include, but
are not limited to the following.
 Outdoor units in which a temperature differential exists as a result of the sun
shining on only one side or part of the foundation.
 Indoor units in which there are temperature gradients on the foundation resulting
from cold or hot air blowing over parts on the foundation.
32
2.2.6 Normal machine unbalanced loads (NB)
It is theoretically possible to balance the turbine – generator rotor to eliminate unbalance
forces during rotation. In practice, however, some unbalance will always exist. Its
magnitude depends on factors determined by design, manufacturing, installation, and
maintenance procedures. These factors may include an axis of rotation which does not
pass through the center of mass of the rotor, deflection of the shaft due to gravity,
uneven thermal expansion, and misalignment during installation, and / or corrosion or
wear of moving parts. The cumulative effect of these factors leads to the unbalanced
forces that occur with the shaft rotational speed. These forces are transmitted to
foundation through the shaft bearings. The effect of the normal machine unbalance loads
on the turbine generator foundation can be evaluated by a dynamic analysis. Dynamic
analysis is recommended for low tuned foundations. The normal machine unbalance
load is
specified as a dynamic forcing function when a dynamic analysis of the foundation is
to be performed
2.2.6.1 Dynamic Forcing Function
For the purpose of defining the normal machine unbalance dynamic load, the turbine
generator rotor can be approximated by a multiply supported shaft with a rotating disc
corresponding to each of the turbine stages and the generator as shown in Figure 2.4.
The forcing function F(t) equation (2.1) is a generic function to determine the dynamic
force applied on the foundation at any operating frequency Ω corresponding to each of
the turbine stages or the generator
33
Where:
F (t )  M i .

G. 2
.sin(.t  i )

(2.1)
Mi= the mass of the rotating mass i
G = e ω, a measure of the balance quality grade of the rotors
e = the rotating mass eccentricity, which equals the distance between the axis of rotation
and the mass center of the rotating mass (see Figure 2.5)
ω = the machine design operating speed in radians / seconds
Ω = the rotational speed in radians / second for which the unbalance force is being
computed
αi
=
the relative phase angle of the unbalance for rotating mass
Figure 2.5. Rotating eccentric mass (Ref. 1)
34
Figure 2.6 Unbalanced forces along shaft with multiple supports. (Ref. 1)
In fig. 2.5, Ω is any operating frequency of the machine such as the starting up, warming
up and shutting down frequency. While in Figure 2.6, the maximum dynamic force is
determined at the machine operating frequency where Ω = ω and equation 2.1 is
simplified to equation 2.2
Where:
F (t )  M i .ei . 2
(2.2)
For turbine generator sets, the balance quality grade is G 2.5 (ref.11). This corresponds
to a G value of 2.5 mm/s. The relative phase angle (αi ) of the unbalance forcing function
corresponding to each stage of the turbine and generator is random and therefore
unknown at the design stages however, its random nature should be considered in the
35
determination of the probable maximum response of the turbine foundation system due
to the normal machine unbalance.
The 2.5 mm/s G value corresponds to a minimum operating unbalance, and the actual
operating unbalance is likely to be larger. The design unbalance should be specified by
the turbine generator manufacturer. G value of (5 mm. /s) may be used when the
manufacturer’s information is not available. For the design unbalance, the maximum
bearing cap deflection should be limited to the trip limit (0.254 mm peak to peak) for
machine from 80% to 120% of operating speed.
2.2.7 Generator emergency torque (QE)
Of the entire short – circuit faults that can occur, a line to line short circuit at the
generator terminals causes the most severe loading of the turbine- generator foundation.
Such a fault occurs when any two of the three generator phase terminals are shorted. The
calculation of the maximum generator air-gap torque during symmetrical (Three
phase)and unsymmetrical (line to line and line to ground) terminal short circuits is
normally performed assuming no electrical damping in order to obtain the greatest
possible forces that can be transmitted to the foundation under different fault conditions.
The results show that the maximum torque resulting from a line-to-line short circuit is
about 25% greater than that caused by a single terminal to ground fault at the terminals of
the same generator.
The loading due to generator short circuits is generally provided either as a forcing
function or as equivalent static forces. The use of equivalent static loads for the
maximum short circuit torque assumes that the foundation is infinitely rigid and
consequently must directly absorb the full impact of the severe shock forces. Since this
36
assumption may result in overdesigning the foundation, the more realistic approach of a
dynamic analysis based on the short circuit torque time function is generally preferred.
2.2.8 Load due to out of phase synchronization (MS)
Out of phase synchronization means that the wave form of the voltage being produced by
the generator does not have the same time relationship with system voltage phaser at the
instant the generator is connected to the system. Faulty synchronization can impose
severe alternating forces on the foundation near the generator. The maximum air-gap
torque resulting from worst case maisynchronization (120 electrical degrees out of phase)
is a function not only of the generator design parameters, but also of the characteristics of
the electrical transmission system to which the generator is connected. If the sum of the
main step-up transformer reactance and the system reactance equals the sub transient
reactance of the generator, the 120 out of phase synchronization causes a shock force on
the foundation roughly equivalent to the maximum line to line short circuit torque
(Ts.c.max). In the case relatively small transformer reactance and a strong system, the
worst-case maisynchronization air-gap torque can lie in the range of 10% to 35% greater
than the Ts.c.max. value. Even if the system and transformer reactance are both considered
to be zero (i.e., the generator is connected directly to an infinitely strong system), the
theoretical maximum maisynchronization torque is only about double the Ts.c.max
amplitude.
The turbine manufacturer will specify the magnitude of this loading in the form of
forcing function or equivalent static forces should be desire to have any part of the
foundation designed for this loading. However, generators are not designed for any
electrical disturbances that are more severe than terminal short circuits. Due to the
37
extremely low probability of faulty synchronization occurring with a sufficiently large
angular discrepancy between generator and system voltage phases to result in an air-gap
torque peak which exceeds the Ts.c.max value, it is an acceptable practice not to consider
the exceptional case of gross maisynchronization as a criterion or foundation design. This
assumes that the effects of worst-case out – of phase synchronization can be covered by
the overall foundation design margins.
2.2.9 Load due to bowed rotor (AB)
A bowed rotor can impose large dynamic forces on the turbine-generator foundation. The
bowed condition of the rotor will create unbalance forces, which are transmitted through
the machine bearings to soleplates. The magnitude of the forces will vary with the square
of the speed, the weight of the rotor, and the amount of eccentricity in the rotor.
A bowed rotor can occur in any turbine section and can be the result of the following
conditions: Usually severe packing rub; water induction; and faliure to put the rotor on a
turning gear when the machine is shut down.
The first condition, severe packing rub, will cause differential temperatures in the rotor,
which will cause the rotor to bend, resulting in the unbalance. The second condition,
water induction, can occur when a slug of water enters the turbine, causing a differential
temperature and bending of the rotor shaft. The third condition can be caused by
improper operation or system failure and not placing the rotor on turning gear operation
while cooling down.
The largest bowed rotor response occurs at the first critical speed for the rotor. The length
of time that it takes for the turbine rotor to pass through the critical speed is a relatively
38
short period while going on line. However, the time is much longer when the machine is
being taken off line and the rotor coasts through the resonant speed.
The probability of bowed rotor is difficult to be estimated however, it is likely that some
degree of bowing will occur during the life of the unit. Since this condition that usually
requires turbine-generator shutdown, it will exist only for the time required for the rotor
to coast down to rest. Therefore, it is any permanent damage to the structure during the
coast down period.
The forces due to a bowed rotor can be calculated with a relationship similar to that for
an unbalanced rotor as follows:
F = M e ω2 (sin ωt)
(2.3)
Where:
F= force due to bowed rotor.
M= mass of rotor.
e = assumed rotor eccentricity, and
ω = critical circular frequency of the shaft or foundation
The loading will be provided in the form of sinusoidal forcing function for the dynamic
analysis or equivalent static loads for a simplified analysis of the foundation.
Some turbine manufacturers assume that a bowed rotor is the worst accidental loading
case of turbine emergency for the high-pressure sections. Other turbine manufacturers
assume that the loss of turbine blade (see next section) is the worst turbine emergency
39
loading case and do not consider a bowed rotor emergency load in their summation of
loads for the turbine.
2.2.10 Load due to missing rotor blade (AM)
A turbine rotor must be balanced dynamically within practical limits in order to ensure
satisfactory turbine operation and cause no adverse effects on the turbine equipment
and/or foundation. However, a more severe unbalance can occur while the unit is in
operation. This emergency unbalance condition is predicated on the unlikely event that a
last row blade in low pressure turbine rotor breaks loose from the rotor. The loss of this
blade, which in a low pressure rotor about 20 inches (500 mm) to over 40 inches (1000
mm) in length, could cause a significant unbalance in the rotor / bearing/ foundation
system . The magnitude of this unbalance is a function of the blade weight, its center of
gravity with respect to the rotor, and the rational speed of the rotor. This force is
transferred to the foundation through the rotor bearing system. Refer to figure 2.4.
As this condition can be postulated to occur in any of the several rows of last row blades,
a separate analysis should be made with a single unbalance equivalent to the loss of one
last row blade applied to the mass point corresponding to each of the last blade rows in
each low-pressure turbine. Since this is an emergency condition that will require turbine
generator shutdown, it will exist only for the time required for the rotor. To coast down to
rest. Therefore, it is sufficient to assure that the stresses in the foundation are low enough
to preclude any permanent damage to the structure during the coast down period.
40
The turbine manufacturer supplies the magnitude and location of the forces due to the
loss or breakage of a last row blade. The loading is provided in the form of a sinusoidal
forcing function for dynamic analysis or equivalent static loads for simplified analysis of
the foundation.
Figure 2.6. Load due to missing rotor blade (Ref. 1)
Not all the previously mentioned loads are going to be utilized in this study. Harmonic
and modal analyses are the only two types of analysis performed in this thesis to
determine: (1) The response of the structure under the machine operating frequency
(Forced vibration). (2) The natural frequency of the structure under the structure and
machine dead load (free vibration).
The required loads for the two types of analysis are: (1) The dead load at sections 2.2.1 &
2.2.3.1 are required to perform the modal analysis. (2) The normal unbalanced load at
section 2.2.6 is required to perform the harmonic analysis.
41
The purpose of mentioning other types of loads in this chapter is to illustrate the different
types of loads applied on this complex structure during the machine operation and
emergency conditions. Practically the forced vibration analysis under the unbalanced
loads is considered the most important check for this type of foundation, Accordingly
The other previously mentioned loads are not considered in the analysis scope of this
study, however such loads are considered the basic loads used in the strength design for
the structural elements of this foundation, it is outside the scope of this study as it is the
last stage in the design of this foundation.
2.3 Response to Dynamic Load of Operation
The loads mentioned at section 2.2 represents all the expected loads that could be applied
on the machine foundation either at normal operating condition or at emergency
conditions. This study concerns by the frequency analysis (Free damped vibration,
section 1.5.1.2 ) and harmonic analysis (Forced damped vibration, section 1.5.2) to
determine the response of the foundation to the unbalanced load generated due to the
rotation of the machine rotating parts and also to ensure that the natural frequency is at a
good margin from the machine operating frequency. It is worth to mention that allowable
vibration amplitude i.e. the response of the foundation to harmonic load, and the
frequency ranges to avoid are set by the machine manufacturer.
To perform frequency analysis only the dead loads of the machine and structure are taken
in consideration to determine the natural frequency of the machine foundation. To avoid
resonance i.e. excessive deformation, to occur, codes of practice (ref. 1, 9, 10, &12) and
most of the turbine generator manufacturers require the natural frequency to be +/- 20%
away from the machine operating frequency.
42
In addition to the dead load mentioned above, the normal machine unbalanced load
(section 2.2.6) is applied as a time dependant dynamic forcing function to perform the
harmonic analysis and determine the structure response. The response is compared with
the allowable vibration amplitude required by the machine manufacturer.
In the following chapters, a comparative study is performed or a real case study using
both the harmonic & frequency analysis to determine the response of the machine
foundation at different damping ratios, element type, element size and concrete strength.
43
Chapter 3
(Case Study)
Finite Element Model for the Steam Turbine Generator Pedestal
3.1 Introduction
The turbine generator concrete pedestal for HITACHI turbine generator machine located
in EL SOKHNA thermal power plant is adopted in this case study. EL SOKHNA thermal
power plant is a unique plant as it is the first thermal supercritical power plant built in
Egypt with 1300MW capacity. Two steam turbine generator units 650MW generating a
total of 1300MW. Each unit consists of one generator, one high-pressure turbine and two
low-pressure turbines, the weight of this set (machine) is about 1700 ton carried on huge
concrete pedestal. This type of machine is very sensitive to vibration, hence it was the
concern of many studies related to machine foundation as mentioned in the literature
review in chapter 1. The sensitivity of the machine is coming from the deflection criteria
required by the manufacturer during the machine operation. For example, HITACHI the
supplier of EL SOKHNA project machine requires 34 micron peak to peak as the
maximum allowable amplitude (deflection) at the bearing locations. If the machine
bearings take more than 34 micron peak to peak amplitude, the machine will stop (trip)
and get out of the network which supplies electricity all over Egypt, which means that
1300 MW will be eliminated from the electricity supplied through the network that
covering all Egypt. The importance of the structure carrying this machine is coming
from the sensitivity of the machine itself and the impact on the whole country or vital
parts of the country in case of the accidental stop of the machine as a result of exceeding
the allowable vibration amplitude specified in its design and required by the
manufacturer. Accordingly, the concrete pedestal that supports such sensitive machine
44
needs to satisfy the machine supplier criteria through accurate design using the
sophisticated modeling techniques through very advanced software packages. The
selection of ANSYS package to perform the dynamic analysis in this study is a result of
realizing how sensitive and important of the machine carried by this structure and the
need to come up with an accurate reliable results using such sophisticated software
package. In addition ANSYS has more computational power as it can provide speedup
ratios that are five to 10 times greater than other software or previous ANSYS releases.
Even complex multiphysics simulations can be performed more quickly and efficiently.
3.2 Structural description
This steam turbine generator (STG) concrete pedestal is classified as a frame foundation
type (sec. 1.1.2). The configuration of the machine itself imposes the type of the structure
carrying it. In the study there are two condensers lying directly underneath the two low
pressure turbines, the height of each condenser is about 12m, so the choice of the frame
system as a structural system is to satisfy the machine configuration in order to perform
its function which is generating electric power in an efficient way. In some few cases, the
manufacturer designs the condenser to be placed beside the machine (turbines &
generator), so in this case the structural engineer can use block type foundation rather
than frame type foundation.
El Sokhna project Steam Turbine Generator (STG) pedestal foundation is a massive
concrete frame structure. It consists of an operating deck (tabletop), nine vertical
elements (eight columns and one wall at the condenser area) and a basemat. The footprint
of the machinery provided by HITACHI controls the layout of the operating deck. The
deck is 42.26m in the longitudinal direction and 13m in the Transverse direction.
45
There are four openings in the deck for the connection of various piping and equipment to
the underside of the STG machine. For tabletop structural members, the longitudinal ones
are identified as girders and transverse ones as beams. Four columns are provided at the
high-pressure turbine area, one wall between the two low-pressure turbines and another
four columns at the generator area. The eight columns and the wall together with the
operating deck girders and beams comprise the lateral force resisting frame system. Base
mat dimensions are sized to suit the physical arrangement of the equipment and the
structural requirement. The base mat is 48 m long in the longitudinal direction and 17.7m
wide in the transverse direction except that at the condenser area the width is 20.9m. The
mat thickness has been selected to be 2.200m except for the trench where the mat
thickness is 1.000m fig.3.1. The layout of the operating deck and base mat is shown in
Figures 3.1 to 3.6.
Fig. 3.1 Isometric view of the STG machine foundation system
46
Fig. 3.2 Plan view of the STG machine foundation system at top surface of the base mat
(EL. +0.000m) (ref. 16)
47
Fig. 3.3 Plan view of the STG machine foundation system at tabletop elevation
+16.000m (ref. 16)
48
Fig. 3.4 Elevation view at Section A-A (ref. 16)
49
Fig. 3.5 Elevation view at Section D-D (ref. 16)
50
Fig. 3.6 Plan view of pile arrangement (ref. 16)
51
3.3 Site conditions and soil properties
El Sokhna project is situated on 250,000m2 plot of land located immediately to the north
of the existing old sokhna power plant. The plant is about 100 Km east of Cairo, and on
the Gulf of Suez. The site is essentially flat with elevation close to sea level, ranging from
about Elevation +6.2m to elevation +1.4m. All elevations are with respect to Egyptian
Surveying Department Datum (ESDD), which is equivalent to Mean Sea Level (MSL).
The soil properties (Table 3.1) used in this study are the actual properties determined in
the geotechnical and subsurface investigation report prepared for El Sokhna project. The
pressure applied on soil from the STG foundation from different loading cases and load
combinations is more than 5 kg/cm2, while the actual bearing capacity for the soil at this
site is 1.5 kg/ cm2. Accordingly, shallow foundation was an excluded choice as the
foundation supporting system for this foundation. The other alternative is to use piles as
the foundation supporting system as shown in Fig. (3.6). Piles used are 800 mm
diameters and according to pile test reports, this 800 mm piles, and 35 m depth can
support design load as 200-ton vertical load (compression), 20-ton lateral load and 80-ton
as vertical load (tension). Based on the soil conditions, it is decided to use the bored piles.
The soil profile contains clay and gravel layers with different depths, so the pile is
designed to take the vertical load as friction and end bearing pile. The static and dynamic
pile stiffness is determined and summarized in Table 3.2.
52
Table. 3.1 Summary of soil properties at the STG foundation area. (Ref. 6)
53
3.3.1 Static and dynamic stiffness determination
Dynamic stiffness values shown in table 3.2 are applied as the lateral & vertical spring
constants for the simulated piles in the ANSYS 3D model of the STG foundation to
perform the harmonic & modal analysis.
Table. 3.2. Dynamic and Static stiffness. (Ref. 6)
Dynamic
Static
1367
710
Axial Stiffness (MN/m)
65.5
25.8
Lateral Stiffness
(MN/m)
3.3.1.1 AXIAL PILE SPRINGS
Calculation of the static and dynamic axial pile springs is determined in the following
subsections. The calculation is carried out for the 35-m long concrete piles.
3.3.1.1.1 Static Axial Pile Spring
For end-bearing piles, the pile shortening under the allowable axial load is given by
ΔL = Qallow·L/(Ac·Ep) (Reference 7, p.620)
or
ΔL = Qallow/kas
Where Ep = 24,855 MPa
(Concrete modulus of elasticity)
Therefore,
kas = Ac· Ep/L = (0.5)· 24,855/(35) = 3.55 x 105 kN/m.
For frictional piles, the pile shortening under the allowable axial load is given by
54
ΔL = Qallow·L/(2·Ac·Ep) (Reference 7, p.622)
or
ΔL =
Qallow/kas
Therefore,
kas = 2·Ac· Ep/L = 2(0.5)· 24,855/(35) = 7.1 x 105 kN/m
3.3.1.1.2 Dynamic Axial Pile Spring
The dynamic axial pile spring stiffness can be calculated from (Ref 24):
k ad = f w1 Ap Ep /(d / 2)
Where d is the diameter of the pile, G is the soil small-strain shear modulus, and fw1 is the
function of Ep/G and L/ (d/2)
L/(d/2) = 35/(0.8/2) = 87.5
Therefore,
fw1 = 0.044
kad = 0.044 x 0.5 x24855 / (0.8/2) = 1367 MN/m
3.3.1.2 Lateral Pile Spring
3.3.1.2.1 Static Lateral Pile Spring
Static lateral pile spring depend on the equation K = P / Δ, so by determining the force (P) and
the deflection (Δ) results from this force, the lateral stiffness K can be determined. For P = 20
kN and Δ = 7.75 mm K = 25.8 MN/m
3.3.1.2.2 Dynamic Lateral Pile Stiffness
The dynamic lateral pile spring can be calculated from (Ref. 24):
Kld = fxl Ip Ep / (d/2) 3
55
Where Ip is moment of inertia of pile cross-section, and fx1 is a function of Ep/G and Poisson’s
ratio (υ) of the soil, Since the upper soils influence the soil stiffness, use high strain G for
upper 10 diameter length. Thus, assuming Sand 1 profile of G will be:
G = 20 MPa
For analysis of lateral pile stiffness, Ep = 24855 MPa
With Ep/G = 24855 / 20 = 1242.75 and υ = 0.35, fx1 = 0.0084 for fixed-head piles and fx1 =
0.00367 for free-head piles. Therefore,
kld = 0.0084 x 0.0201 x 24855 / (0.8/2)3 = 65.5 MN/m.
3.4 Finite element 3D model
To capture the foundation behavior under the applied machine static & dynamic loads, a linear
elastic finite element model is created using ANSYS package. As shown in Fig.3.8, the finite
element model of the STG foundation is comprised of solid elements (SOLID45, SOLID 92 &
SOLID 95) for the super structure. The supporting piles are modeled using spring-damper
elements (COMBIN14). In this manner, the horizontal and vertical dynamic stiffness of piles
are represented as springs at each pile location (Table 3.2). Three solid element types and one
spring damper element are used in this study to determine the variation of using such types of
element with respect to varying damping ratios and element sizes. These element types are
discussed in the following sub-sections
56
3.4.1 SOLID 45 [8-nodded element]:
Solid 45 is used for the 3D modeling of solid structures. Eight nodes having three degrees
of freedom at each node define the element (Fig. 3.8). These degrees of freedom are the
translations in the nodal x, y and z directions. Solid 45 has plasticity, creep swelling,
stress stiffening, large deflection, and large strain capabilities.
Fig. 3.8 Solid 45 (3D Structural Solid) (Ref. 4)
The geometry, node locations, and the coordinate system for this element are shown in
Fig 3.8. Eight nodes and the isotropic material properties define the element. Orthotropic
material directions correspond to the element coordinate directions. Pressures may be
input as surface loads on the element faces as shown by the circled numbers on Fig 3.8.
Positive pressures act into the element. Temperatures may be input as element body loads
at the nodes.
3.4.2 SOLID 92 [10-nodded element]:
SOLID92 has a quadratic displacement behavior and is well suited to model irregular
meshes (such as produced from various CAD systems). Ten nodes having three degrees
of freedom at each node define the element. These degrees of freedom are the translations
57
in the nodal x, y and z directions. The element also has plasticity, creep, swelling, stress
stiffening, large deflection, and large strain capabilities.
Fig. 3.9 Solid 92 (3D Structural Solid) (Ref. 5)
The geometry, node locations, and the coordinate system for this element are shown in
Fig. 3.9. Beside the nodes, the element input data includes the orthotropic material
properties. Orthotropic material directions correspond to the element coordinate
directions. Pressures may be input as surface loads on the element faces as shown by the
circled numbers on Fig.3.9. Positive pressures act into the element. Temperatures may be
input as element body loads at the nodes.
3.4.3 SOLID 95 [20-noded element]:
Solid 95 is a higher order version of the 3D 8-node and 10-node solid element Solid 45
and solid 92 respectively . It can tolerate irregular shapes without as much loss of
accuracy. Solid 95 elements have compatible displacement shapes and are well suited to
model curved boundaries. Ten nodes having three degrees of freedom at each node define
the element. These degrees of freedom are the translations in the nodal x, y and z
directions. Solid 95 has plasticity, creep, stress stiffening, large deflection, and large
strain capabilities.
58
Fig. 3.10 Solid 95 (3D Structural Solid) (Ref. 4)
The geometry, node locations, and the coordinate system for this element are shown in
Fig 3.10. A prism-shaped element may be formed by defining the same node numbers for
nodes K, L, and S; nodes A and B; and nodes O, P, and W. A tetrahedral-shaped element
and a pyramid-shaped element may also be formed as shown in Fig.3.10. Besides the
nodes, the element input data includes the orthotropic material properties. Orthotropic
material directions correspond to the element coordinate directions.
Pressures may be input as surface loads on the element faces as shown by the circled
numbers Fig.3.10. Positive pressures act into the element. Temperatures may be input as
element body loads at the nodes.
59
3.4.4 Combin14 [spring-damper element]:
Combin14 has longitudinal or torsional capability in 1-D, 2-D, or 3-D applications. The
longitudinal spring-damper option is a uniaxial tension-compression element with up to
three degrees of freedom at each node: translations in the nodal x, y, and z directions. No
bending or torsion is considered. The torsional spring-damper option is a purely
rotational element with three degrees of freedom at each node: rotations about the nodal
x, y, and z axes. No bending or axial loads are considered. The spring-damper element
has no mass. The spring or the damping capability may be removed from the element
Fig. 3.11 Combin14 (spring-damper) (Ref. 4)
The element is defined by two nodes and a spring constant (k). The damping capability is
not used for static or undamped modal analyses. The longitudinal spring constant should
have units of Force/Length.
60
Fig. 3.12 Finite element model of the machine foundation
The STG machine is installed on the pedestal foundation through sole plates. To account
for the machine rigidity at the machine foundation interface, rigid regions are defined on
the top surface of each sole plate as shown in the Figure 3.13.
Rigid regions are applied by connecting all the node at the sole plate location by master
node, that guarantee that all the nodes at the sole plate location responds by the same
manner when applying and force to the rigid region master node. This assure that the
machine , bearings and sole plates (embedded metal inside concrete) respond as one unit
to the forces applied on it either static force or dynamic force.
Bearing points of the machinery are connected to centroids of the sole plates with rigid
links using 3D elastic beam elements (BEAM44), this element can take force in uniaxial
61
direction without allowing for bending or torsion. In total, 19 rigid links are generated.
Figures 3.13, 3.14 & 3.15 illustrates the rigid regions and rigid links used in the finite
element model.
Fig. 3.13 Rigid regions location at the tabletop of the foundation model
62
Fig. 3.14 Rigid links & machine bearing locations
63
Fig. 3.15 The bearings connected to the table top through the rigid links
3.5 Scope of analysis in the current Study:
The purpose of this study is to determine the dynamic response of the foundation by
performing dynamic analysis represented in the modal (free vibration) and harmonic
(forced vibration) analysis considering the change of the following parameters in the
ANSYS numerical model:
a – Damping ratios, a range of damping ratios will be considered. The analysis will start
with 2% damping ratio with 0.5% increase in the damping ratio. The usual practice of
such kind of analysis is to consider 2% damping ratio. Other values for the damping
ratios are examined in this study to determine the response of the structure.
64
b – Element type, Study the effect of using different elements with 8, 10 and 20 nodes.
The level of accuracy of the results changes with the change in the element number of
nodes. The level of accuracy is important in such types of analysis because the machine
manufacturer criterion for the allowable vibration amplitude (deflection) ranges from 10
to 30 microns, accordingly any change in the element node number affect the response
(amplitude) of the STG pedestal.
c – Mesh size, study the effect of using different mesh sizes 500, 800 & 1100 mm. As
mentioned in the previous point about the sensitivity of the response (amplitude) of the
structure to dynamic force. The mesh size is considered as effective factor in the accuracy
of determination of the response of STG pedestal.
Frequency analysis is not expected to be significantly affected by the change in the
damping ratio. The damping ratio only significantly affect the response of the structure in
the harmonic analysis (forced vibration).
Element type and mesh size also have a significant effect on: (1) the time consumed in
the calculation, (2) the cost of preparing the calculation represented in the engineer-hours
spent in running such type of problem and (3) the high performance computer required to
solve such problem. For example by using 10 nodded element type with mesh size
500mm, the time consumed to complete a full sweep analysis is about 50 hours.
Dynamic analyses performed is to assess the adequacy of the STG pedestal foundation to
support the operating machinery and sustain the machinery associated dynamic loads
within the limits specified by the machine supplier. According to vendor requirement,
there are two criteria for the proposed foundation design to meet:
65
The fundamental natural frequencies of the STG machine-foundation system in each
direction shall be at least 20 % away from the machine operating speed of 50 Hz.
The foundation vibration amplitudes shall be within the allowable limit of 0.017 mm at
the machine rated speed.
In order to address each of the aforementioned criteria, modal analysis is performed in
which natural frequencies and associated modes shapes are first computed up to 1.2 times
the machine operating speed as required by the machine supplier. This is followed by
harmonic analyses to verify that the peak amplitudes of the bearing centers are within
allowable limits for the operational unbalanced loads.
66
Chapter 4
Analysis of Results
4.1 MODAL ANALYSIS:
Modal analysis is conducted to obtain the modal frequencies of the STG pedestal in which
the natural frequencies are extracted up to 1.4 times of the machine operating frequency.
Furthermore, the effective translational direction (UX, UY& UZ) of the first 40 modes are
calculated. The results indicate that the cumulative effective masses of the modes below
30Hz are already very close to the total mass of the STG foundation and contributions
from higher modes can be considered negligible. This clearly demonstrates that the
fundamental frequencies are at least 25% away from the normal operating speed (50Hz)
which satisfies the machine manufacturer criteria (Ref. 17). However, it should be noted
that the impact of local structural modes on the vibration amplitude of the STG pedestal
foundation might hardly be represented by effective mass. Therefore, a harmonic analysis
over frequency range of ± 20% of operating speed 50Hz is performed in section 4.2.
The modal analysis is performed considering the changes in the parameters mentioned at
the previous chapter, section 3.5.
The modal analysis results for 2% damping ratio with solid-45 (8-nodded solid element)
corresponding to mesh size 500 mm, 800 mm & 1100 mm are shown in Tables 4.1 to
4.6. Detailed tables to illustrate the results are in appendix B
67
Table 4.1 Frequency corresponding to mode shapes for damping 2%,
mesh size 500 mm – 8-nodded element
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.263
3.348
3.560
7.114
7.355
8.627
10.740
12.604
14.335
14.567
16.915
17.328
18.587
18.777
19.115
20.339
21.179
22.252
22.916
23.471
23.693
23.972
25.038
25.809
25.903
26.318
27.981
28.458
28.621
28.884
29.288
30.068
30.181
30.763
31.420
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
31.962
32.937
33.364
34.442
34.932
35.386
35.744
36.055
37.461
37.872
38.973
39.204
40.076
40.218
40.946
41.431
42.454
42.940
43.194
43.529
43.791
44.858
44.906
46.111
46.272
46.286
46.638
46.871
47.187
47.593
48.424
48.902
49.429
49.953
51.018
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
Freq
(Hz)
51.401
52.245
52.360
52.498
52.911
53.459
53.766
53.958
54.542
55.325
55.816
56.241
56.481
56.964
57.185
57.517
57.955
58.444
58.732
59.122
59.752
60.182
60.675
61.290
61.983
62.339
62.857
63.132
63.687
63.949
64.245
64.803
65.135
65.318
66.145
68
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
66.837
66.875
67.726
67.975
68.493
68.960
69.294
69.428
70.000
70.523
70.779
70.833
70.978
71.315
71.575
71.728
72.149
72.237
72.322
72.479
73.167
73.354
73.553
73.932
73.995
74.349
74.520
74.989
75.416
75.487
75.871
75.984
76.272
76.580
76.777
Table 4.2 Effective masses corresponding to frequency for the first 40 modes for damping 2%,
mesh size 500 mm – 8-nodded element
UZ
1.58E-04
2.36E-04
7.35E-10
5.99E-04
4.35E-03
3.56E-03
2.33E-03
4.22E-03
11.9331
0.489402
1.96E-03
1.10E-03
0.106115
4.95E-02
7.57E-02
5.19E-03
4.87E-03
3.12E-03
2.96E-02
1.57E-02
5.49E-02
0.39668
0.231191
8.19E-03
1.68E-03
5.97E-03
8.36E-03
1.82E-02
1.85E-04
0.196538
4.29E-03
1.22E-02
4.12E-02
4.46E-02
4.13E-02
8.45E-02
7.54E-03
2.92E-04
1.01E-02
1.36E-04
1.39E+01
98%
UY
2.38E-02
12.8363
0.335974
0.525275
6.17E-02
0.310454
7.05E-05
1.72E-04
5.66E-06
1.31E-07
2.60E-07
9.97E-07
4.02E-05
3.23E-05
3.98E-06
4.53E-05
1.75E-04
1.69E-06
3.28E-06
5.85E-06
2.46E-05
1.08E-05
1.83E-09
1.59E-04
5.36E-05
1.90E-06
4.56E-04
4.47E-05
4.26E-05
1.67E-05
1.79E-06
3.15E-05
1.88E-10
5.77E-05
7.17E-07
4.22E-07
4.84E-05
3.10E-06
2.03E-05
6.78E-06
1.41E+01
99%
UX
1.28E+01
1.57E-02
4.35E-02
7.71E-02
1.11036
6.27E-03
1.50E-05
1.88E-06
1.71E-05
2.21E-04
5.88E-05
6.80E-08
2.49E-05
2.57E-05
3.34E-04
1.95E-06
8.47E-07
7.86E-07
4.96E-07
9.83E-07
3.77E-05
1.56E-04
7.98E-05
2.22E-07
3.08E-05
5.83E-06
9.95E-06
7.94E-05
4.74E-07
1.50E-05
1.12E-05
1.34E-05
7.16E-06
1.01E-06
8.00E-05
1.18E-05
6.96E-05
2.69E-05
5.04E-06
1.47E-05
1.41E+01
99%
Mode
Freq (Hz)
No.
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
69
Table 4.3 Frequency corresponding to mode shapes for damping 2%,
mesh size 800 mm – 8-nodded element
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.344
3.395
3.629
7.513
7.784
8.989
11.335
13.667
14.693
15.021
17.523
18.295
19.039
19.586
19.992
21.107
22.263
23.317
24.024
24.646
24.926
26.032
26.592
26.844
27.259
27.298
29.243
29.600
29.853
30.097
31.241
31.485
31.846
32.079
33.134
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
33.770
34.367
34.737
36.213
36.646
37.314
37.422
37.803
39.049
39.376
40.630
40.870
41.379
41.981
42.744
42.952
44.098
44.316
44.696
45.093
45.862
46.008
46.862
47.436
47.571
48.134
48.657
48.775
49.200
49.271
49.605
49.932
50.347
51.753
51.930
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
Freq
(Hz)
52.394
52.816
53.646
54.479
54.876
55.149
55.960
56.208
56.889
57.464
57.792
57.880
58.646
58.948
59.216
59.283
59.737
60.737
61.026
61.354
61.922
62.341
62.523
62.894
63.013
64.036
64.234
64.794
65.079
65.303
65.440
65.704
66.210
66.709
67.164
70
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
67.512
68.206
68.382
68.697
69.055
69.541
70.304
70.892
70.968
71.525
71.972
72.403
72.642
73.014
73.119
73.526
73.719
73.941
74.137
74.396
74.453
74.648
74.949
75.104
75.303
76.005
76.413
76.761
76.904
77.248
77.500
77.879
78.290
78.527
78.617
Table 4.4 Effective masses corresponding to frequency for the first 40 modes for damping 2%,
mesh size 800 mm – 8-nodded element
UZ
1.37E-04
2.04E-04
7.61E-07
1.15E-03
4.80E-03
3.51E-03
2.33E-03
1.43E-02
1.25E+01
8.17E-02
2.79E-03
7.22E-04
4.76E-03
7.61E-02
7.63E-02
4.03E-03
5.33E-03
1.37E-02
4.47E-02
1.02E-01
2.38E-01
2.63E-01
9.41E-03
2.07E-02
8.19E-03
3.01E-05
7.38E-03
8.69E-02
4.93E-04
1.30E-01
6.24E-02
9.51E-05
1.03E-02
4.87E-02
7.88E-02
5.35E-04
1.39E-04
8.21E-03
1.84E-02
8.50E-03
1.39E+01
98%
UY
6.33E-02
1.32E+01
9.89E-02
4.86E-01
3.50E-02
2.28E-01
1.27E-06
6.94E-05
5.62E-06
1.67E-07
1.55E-07
1.25E-05
5.62E-05
8.50E-07
9.40E-07
3.19E-05
1.41E-04
7.73E-07
1.40E-05
1.98E-05
2.49E-05
6.39E-06
2.53E-05
2.41E-05
8.31E-05
3.09E-05
3.55E-04
1.73E-05
2.23E-05
1.79E-05
1.42E-05
1.46E-06
7.64E-05
3.80E-06
4.46E-07
7.24E-06
7.09E-06
5.02E-05
6.45E-06
3.43E-05
1.41E+01
99%
UX
1.31E+01
5.33E-02
7.51E-02
3.03E-02
8.65E-01
6.29E-03
7.92E-06
1.55E-06
3.03E-05
1.17E-04
6.26E-05
6.93E-07
1.23E-05
1.53E-05
3.00E-04
3.16E-06
1.32E-06
4.11E-06
6.36E-06
6.34E-05
7.46E-05
1.93E-05
1.73E-05
8.22E-06
1.81E-05
1.63E-07
8.46E-06
2.07E-05
2.47E-06
1.64E-05
2.33E-05
5.96E-06
2.08E-05
1.41E-05
2.73E-07
6.24E-05
8.41E-05
1.06E-06
2.08E-05
3.02E-10
1.41E+01
99%
Mode
Freq (Hz)
No.
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
71
Table 4.5 Frequency corresponding to mode shapes for damping 2%,
mesh size 1100 mm – 8-nodded element
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.397
3.420
3.666
7.734
8.125
9.246
11.817
14.496
14.951
15.336
18.024
18.942
19.591
20.255
20.819
21.744
23.237
24.191
25.017
25.467
26.122
27.041
27.772
28.161
28.392
28.799
30.621
30.776
31.330
31.539
32.817
32.875
33.206
33.559
34.377
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
35.388
35.937
36.464
37.953
38.501
38.946
39.375
39.828
41.158
41.458
42.614
43.131
43.792
44.394
44.877
45.193
46.044
46.198
46.461
46.860
47.989
48.515
48.966
49.929
49.950
50.248
50.646
50.716
51.011
51.315
51.445
51.747
52.581
53.236
54.046
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
Freq
(Hz)
54.905
54.948
55.912
56.330
56.726
57.281
58.212
58.830
59.406
59.675
60.490
60.853
60.942
61.352
61.895
62.231
62.673
62.996
63.359
64.106
64.249
64.820
64.998
65.041
65.192
65.693
66.155
66.818
67.147
67.688
67.947
68.319
68.463
68.817
69.527
72
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
69.745
70.029
70.671
70.853
71.636
72.254
72.537
73.108
73.243
73.379
73.715
73.942
74.325
74.438
74.646
74.929
75.177
75.424
75.793
75.981
76.270
76.508
76.669
76.960
77.292
77.484
77.773
78.269
79.169
79.382
79.729
79.831
79.972
80.222
80.483
Table 4.6 Effective masses corresponding to frequency for the first 40 modes for
damping 2%, mesh size 1100 mm – 8-nodded element
UZ
1.27E-04
1.80E-04
2.12E-06
1.78E-03
4.87E-03
3.34E-03
2.60E-03
8.91E-02
1.25E+01
1.23E-01
3.25E-03
8.25E-04
4.48E-04
4.73E-02
7.21E-02
5.14E-03
5.24E-03
1.64E-02
4.89E-04
1.75E-01
2.75E-01
1.68E-01
1.29E-02
8.36E-03
1.83E-03
2.49E-02
7.04E-03
9.48E-02
7.07E-02
3.48E-02
3.89E-02
6.81E-03
4.60E-02
9.91E-03
5.60E-02
6.87E-05
2.22E-04
1.06E-02
3.44E-02
1.44E-04
1.40E+01
98%
UY
0.169179
13.1976
5.43E-02
0.466307
1.74E-02
0.189501
3.08E-07
4.60E-05
7.01E-06
2.66E-07
3.64E-08
3.72E-05
2.58E-05
1.24E-07
6.46E-07
3.72E-05
8.82E-05
4.41E-07
1.18E-05
2.58E-05
2.13E-05
3.92E-06
3.65E-05
9.12E-06
6.39E-06
8.09E-05
1.96E-04
6.45E-07
2.87E-05
8.52E-05
6.72E-07
7.77E-06
2.95E-05
4.21E-05
4.08E-06
1.49E-06
9.26E-06
3.31E-05
1.33E-05
1.19E-05
1.41E+01
99%
UX
1.31E+01
1.53E-01
1.10E-01
9.34E-03
7.13E-01
5.99E-03
5.28E-06
2.04E-06
2.51E-05
6.50E-05
5.37E-05
2.98E-06
5.42E-06
3.02E-05
2.37E-04
5.16E-06
1.30E-06
3.60E-06
2.91E-05
4.63E-05
3.16E-05
4.13E-05
1.41E-05
1.14E-06
3.50E-07
3.35E-06
5.68E-06
5.57E-06
3.17E-06
5.30E-06
7.99E-09
3.08E-05
3.00E-06
1.08E-05
2.72E-07
1.36E-05
1.14E-04
1.58E-06
2.16E-05
4.81E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.397
2
3.420
3
3.666
4
7.734
5
8.125
6
9.246
7
11.817
8
14.496
9
14.951
10
15.336
11
18.024
12
18.942
13
19.591
14
20.255
15
20.819
16
21.744
17
23.237
18
24.191
19
25.017
20
25.467
21
26.122
22
27.041
23
27.772
24
28.161
25
28.392
26
28.799
27
30.621
28
30.776
29
31.330
30
31.539
31
32.817
32
32.875
33
33.206
34
33.559
35
34.377
36
35.388
37
35.937
38
36.464
39
37.953
40
38.501
SUM
Sum / Total mass
73
Tables 4.1, 4.3 & 4.5 summarize the structure frequency corresponding to each of the
140 mode shapes, this table is essential in determining the margin of which the natural
frequency value located with respect to the machine operating frequency. Tables 4.2, 4.4
& 4.6 summarize the frequency corresponding to the first 40 mode shapes, in addition to
the effective masses excited at each mode shape in X, Y & Z directions. This table is
essential in determining the natural frequency as it defines the mode shapes that capture
most of the masses of the structure.
The values shown in Tables 4.1 to 4.6 and appendix B indicate that the cumulative
effective masses of the modes below 30Hz are already very close to the total mass of the
STG foundation and it is clear from the results that the change in damping ratio, mesh
size and element node number has no effect on the cumulative mass corresponding to
frequencies from 1 Hz to below 30 Hz.
Figures from 4.1 to 4.5 are showing the mode shapes for the first 5 modes for damping
2%, mesh Size 500 mm and 8-nodded element type. These first 5 mode shapes of the
STG foundation captures 99% of the foundation and machine masses. The displayed
mode shapes shown in the figure below are the vector sum of the translation in X & Y
axes.
74
Fig. 4.1 First mode shape, 2% damping, mesh Size 500 mm and 8-nodded element type.
75
Fig. 4.2 Second mode shape, 2% damping, mesh Size 500 mm and 8-nodded element type.
76
Fig. 4.3 Third mode shape, 2% damping, mesh Size 500 mm, and 8-nodded element type.
77
Fig. 4.4 Fourth mode shape, 2% damping, mesh Size 500 mm, and 8-nodded element type.
78
Fig. 4.5 Fifth mode shape, 2% damping, mesh Size 500 mm, and 8-nodded element type.
79
4.1.1 Modal analysis results summary
Table 4.7 summarizes the results for all the modal (frequency) analysis runs performed to
determine the effect of the change in damping ratio, mesh size and element type on the
fundamental frequency of the STG foundation.
As shown in the Table 4.7, the changes in the fundamental frequency values reflect the
change in damping ratio, mesh size and element type. It is clear from the table that the
change in the damping ratio has no effect on the fundamental frequency, for the other
parameters, changes in the natural frequency values is observed due to the changes in the
mesh size and element type. For mesh sizes (500mm to 1100mm) the fundamental
frequency values increase by 1% to 2% for the 8 nodded elements and 0.4% to 0.6% for
the 10 & 20 nodded elements.
However, these changes are not significant to this type of analysis, but it can give a
direction that mesh size & element type have no real tangible effect on the results
obtained from this analysis. Based on this result, less complex finite element model could
be used in such type of analysis without significant change on the results.
80
Table 4.7 Modal Analysis Results Summary
Mesh size 500mm
8
10
20
nodded
nodded
nodded
Fundamental
frequency
3.263
3.143
3.143
Mesh size 500mm
8
10
20
nodded
nodded
nodded
Fundamental
frequency
3.263
3.143
3.143
Mesh size 500mm
8
10
20
nodded
nodded
nodded
Fundamental
frequency
3.263
3.143
3.143
Mesh size 500mm
8
10
20
nodded
nodded
nodded
Fundamental
frequency
3.263
3.143
3.143
Damping 2%
Mesh size 800mm
8
10
20
nodded
nodded
nodded
3.344
3.164
3.164
Damping 3%
Mesh size 800mm
8
10
20
nodded
nodded
nodded
3.344
3.164
3.164
Damping 4%
Mesh size 800mm
8
10
20
nodded
nodded
nodded
3.344
3.164
3.164
Damping 5%
Mesh size 800mm
8
10
20
nodded
nodded
nodded
3.344
3.164
3.164
Mesh size 1100mm
8
10
20
nodded
nodded
nodded
3.397
3.178
Mesh size 1100mm
8
10
20
nodded
nodded
nodded
3.397
3.178
3.397
3.178
3.178
Mesh size 1100mm
8
10
20
nodded
nodded
nodded
3.397
3.178
The machine supplier (ref. 17) stipulates that the vibration severity at machine bearing
support points should be less than the allowable zero-to-peak amplitude of 17 μm ( 34 μm
is peak-to-peak ) at the normal operating speed (50 Hz). It further specifies that for
various speeds up to 120% that is considered to have sufficient margin for normal
operating practice, the allowable zero-to-peak amplitude is 14.25 μm (28.5 μm peak-topeak). The dynamic unbalance loads caused by a mass and corresponding eccentricity are
81
3.178
Mesh size 1100mm
8
10
20
nodded
nodded
nodded
4.2 Harmonic Analysis :
provided as follows:
3.178
3.178
Table 4.8 Dynamic unbalanced loads (Ref. 17)
D ynamic Load : Wd
UNIT : KN
No. 8
74.50
No. 7
83.40
No. 6
53.90
No. 5
51.00
No. 4
51.00
No. 3
46.10
No. 2
41.20
No. 1
24.50
BR G. No.
Wd
Figure 4.6 sectional elevation showing the locations of bearings from 1 to 8 (ref. 17).
The unbalance loads produced by a rotor act on the machine bearing points first and then
go to the supporting STG foundation. At each bearing point, the dynamic unbalance loads
are idealized as two sinusoidal forces lagging each other by 90 degrees as in Eqs. (4.1)
and (4.2), in which F v and F h are the vertical and horizontal force component
respectively, e is the mass eccentricity with respect to the axis of rotation, Mr is the rotor
82
mass, and Ω is the rotational speed. Since the net effects of these dynamic forces imparted
on the foundation are of a major concern, equivalent unbalance loads obtained at the
machine sole plate locations are applied to the finite element model instead of applying
these dynamic unbalance forces directly to the bearing points.
FV  e.M r ..(sin t)
(4.1)
Fh = e.M r ..(sin t-π/2)
(4.2)
The vertical dynamic forces are directly translated to the corresponding machine sole
plates while the horizontal dynamic forces are manifested as a combination of horizontal
forces and moments due to the offset distance between the centerline of the machine rotor
shaft and the top surface of the sole plates. The force acting at a node (FNi) of an element
in a particular contact (loading) volume is calculated as follows:
FNi 
Fi
N
Where F Ni
(4.3)
is the force acting in node i, F i
is the total unbalance load acting in a
particular loading volume and N is the total number of interior nodes of the contact
(loading) volume. Coupling moments are distributed in the interior nodes of each of the
contact volumes (i.e. loading points).
As the unbalance loads act on the bearings in a random fashion with different phase
angles, the dynamic responses of the STG foundation are examined using the square-rootsum-of-the-squares (SRSS). The SRSS method involves an assumption that the
83
foundation responses due to dynamic loads at each bearing point are independent of
responses at any other bearing points. Obtained results are then combined using Eq. (4.4):
U.i,max =
 uij
2
(4.4)
j
Where Ui, max is the peak amplitude at bearing i and uij is the peak deflection at bearing (i)
due to the unbalanced load applied at bearing j. For each frequency, the dynamic load
should be using the equation below:
Dynamic load for each rotating speed = (Dynamic load for 3000 rpm) x (rotating speed /
3000)2
(4.5)
The harmonic analysis is performed following the criteria described above at section 4.2
and by applying the dynamic unbalanced loads (Table 4.4) at the soleplates which
support the eight bearings carrying the STG machine to determine the horizontal and
vertical response for each sole plate to the machine unbalanced loads. To cover the +/20% frequency range required in the manufacturer criteria (ref. 17), harmonic analysis is
performed at frequency range from 40 Hz to 60 Hz with frequency step equal 2.
In this study, harmonic analysis is performed to determine the response due to changes in
damping ratio, mesh size & element type. The results for the transverse and vertical
responses corresponding to frequency for each sole plate are plotted at appendix A.
Figures 4.7 to 4.12 show the harmonic analysis results at 2% damping ratio with solid-45
(8-nodded solid element) corresponding to mesh size 500 mm, 800 mm & 1100 mm.
84
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Figure 4.7 Response to harmonic analysis in horizontal direction, Damping 2%:
Mesh Size 500mm – 8-Nodded Element. MAX(Y) = 0.012mm
85
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Figure 4.8 Response to harmonic analysis in vertical direction, Damping 2%:
Mesh Size 500mm – 8-Nodded Element. MAX(Z) = 0.01133mm
86
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Figure 4.9 Response to harmonic analysis in horizontal direction, Damping 2%:
Mesh Size 800mm – 8-Nodded Element. MAX(Y) = 0.00956 mm
87
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Figure 4.10 Response to harmonic analysis in vertical direction, Damping 2%:
Mesh Size 800mm – 8-Nodded Element. MAX(Z) = 0.00893 mm
88
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Figure 4.11 Response to harmonic analysis in horizontal direction, Damping 2%:
Mesh Size 1100mm – 8-Nodded Element. MAX(Y) = 0.00926 mm
89
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Figure 4.12 Response to harmonic analysis in vertical direction, Damping 2%:
Mesh Size 1100mm – 8-Nodded Element. MAX(Z) = 0.00897 mm
As mentioned above, plots shown at figures 4.7 to 4.12 represents the horizontal response
(shown on y-axis, Figures 4.7, 4.9 & 4.11), and vertical response (shown on y-axis,
Figures 4.8, 4.10 & 4.12) for all the soleplates supporting the machine bearings (shown at
the legend) due to the machine unbalanced operational loads at frequency range 40 Hz to
60 Hz (shown at x-axis).The machine manufacturer limit that shouldn’t be exceeded is
represented by the curve called HITACHI at the legend (ref. 17).
90
4.2.1 Harmonic analysis results summary
Table 4.9 summarizes the results for all the harmonic analysis runs that performed to
determine the effect of the change in damping ratio, mesh size and element type on the
response under the dynamic unbalanced machine operating loads at +/- 20% frequency
range of the STG foundation.
As shown in the table 4.9, the changes in the transverse and vertical response (deflection)
values reflect the change in damping ratio, mesh size, and element type. It is clear from
the table that for the same mesh size & element type, the increase in the damping ratios
from 2% to 5% results in decreasing the horizontal displacement by a range from 10% to
15% while the vertical displacement decreases by a bigger range from 16% to 32%. Also
for the damping ratios (2% to 5%) and mesh sizes (500 mm to 1100 mm) the vertical and
horizontal displacements have the same values for the 10-nodded & 20-nodded elements.
While for the damping ratios (2% to 5%) and mesh sizes (500 mm to 1100 mm) the
vertical and horizontal displacements for the 8-nodded elements are 2% to 20% less than
the values of 10 & 20 nodded elements.
Based on the above results, it is determined that the damping ratio has a significant effect
on the structure response in the harmonic analysis of the machine foundation, specially
for turbine generator foundation due to the tight limit required by the machine
manufacturer which is 17 micron (Allowable vibration amplitude, ref. 17). Also for the
10-nodded & 20-nodded elements, no significant change in the structure response
observed when the damping ratio or the mesh size have changed, which is not the case
with the 8-nodded element. This could help in using the 10-nodded element in such
analysis type to save time in the analysis and calculation.
91
Table 4.9 Harmonic Analysis Results Summary.
Damping 2%
Mesh size 800mm
Mesh size 500mm
HL
displacement
VL
displacement
8
nodded
10 nodded
0.012
0.01133
20 nodded
10 nodded
20 nodded
0.01194
0.01033
0.00956
0.01094
0.01094
0.00926
0.01139
0.01139
0.01034
0.01034
0.00893
0.01006
0.01006
Damping 3%
Mesh size 800mm
0.00897
0.01131
0.01131
Mesh size 500mm
HL
displacement
VL
displacement
8
nodded
10 nodded
0.00918
0.00879
20 nodded
10 nodded
20 nodded
0.00903
0.00903
0.00788
0.00869
0.00869
0.00713
0.00907
0.00908
0.00817
0.00817
0.00761
0.00851
0.00851
Damping 4%
Mesh size 800mm
0.00714
0.00896
0.00896
8
nodded
10 nodded
0.00756
0.0073
Mesh size 1100mm
8
20
nodded
10 nodded nodded
20 nodded
8
nodded
10 nodded
20 nodded
0.00751
0.00751
0.00676
0.00743
0.00743
0.00609
0.00765
0.00765
0.00698
0.00698
0.00662
0.00737
0.00737
Damping 5%
Mesh size 800mm
0.0061
0.00752
0.00752
Mesh size 500mm
HL
displacement
VL
displacement
Mesh size 1100mm
8
20
nodded
10 nodded nodded
8
nodded
Mesh size 500mm
HL
displacement
VL
displacement
Mesh size 1100mm
8
20
nodded
10 nodded nodded
8
nodded
8
nodded
10 nodded
0.00652
0.00633
Mesh size 1100mm
8
20
nodded
10 nodded nodded
20 nodded
8
nodded
10 nodded
20 nodded
0.00655
0.00655
0.00596
0.00659
0.00659
0.00538
0.00668
0.00668
0.00635
0.00635
0.00589
0.00653
0.00653
0.00537
0.00655
0.00655
92
4.3 Seismic Analysis:
In addition to the dynamic analysis performed in the above sections, evaluation to the
response of the foundation to seismic effect is considering change in the mesh sizes
(500mm, 800mm & 1100mm) using two approaches is performed:
First approach, by applying the seismic force at the machine anchorage locations.
Second approach, by Applying the seismic force at the center of gravity of the machine.
Seismic Coefficients are determined using the equivalent static theory according to IBC
(International Building Code) and ASCE-7-02 (American Society of Civil Engineers –
Minimum Design Loads for Buildings and Other Structures). Appendix C shows the
calculation of the seismic forces used in the ANSYS model to determine the above
mentioned approach. Calculation of the seismic coefficients are shown in appendix C.
The structure response results are shown below at table 4.10 and graphically shown at
fig. 4.13 & 4.14
Table 4.10 Seismic Analysis Response Results Summary
Max.Deflection
(seismic force applied at Sole plate)
12.546mm
Max.Deflection
(seismic force applied at rigid links)
12.254mm
93
Fig. 4.3 The Deflection due to seismic applied on sole plates.
94
Fig. 4.14 The Deflection due to seismic applied on machine CG at rigid links.
As shown from (fig. 4.13 & fig. 4.14) the deflection results from applying seismic force
at the sole plates is about 2% more than the deflection results from applying seismic force
at the center of gravity of the machine. This is due to the small distance between the
foundation tabletop and the machine, the center of gravity of the machine located 900mm
above the foundation elevation.
95
4.4 High Strength Concrete:
In this section concrete with different compressive strength has been examined to
determine the response of the structure under harmonic excitation with respect to the
change in the compressive strength of the concrete. The change in the compressive
strength of the concrete is determined by changing the value of the elastic modulus (E)
Table 4.11 Harmonic Analysis Response Results Summary (using High strength
concrete).
Horizontal displacement
(mm)
Vertical displacement
(mm)
32 MPa
50 MPa
75 Mpa
0.00655
0.00678
0.00651
0.00635
0.00665
0.00653
It is observed from Table 4.7 that the difference in response due to the changes in the
compressive strength is minor and this can be justified by the fact that the deflection is
affected by the applied force and the stiffness. The case here that the stiffness is only
influenced by changing the elastic modulus of concrete (E). The difference in deflection
to be significant, the change in the elastic modulus should be significant, also the inertia
(I) and the length (L) of the structural element are also have an influence on the stiffness,
so in order to make tangible changes in the stiffness, both the inertia and the length of the
structural elements should be changed and this doesn't considered in the case here, so the
change in deflection was minor.
96
Chapter 5
Summary and Conclusion
5.1 Summary
The purpose of this thesis is to highlight on the machine foundations types, applied loads
and behavior under dynamic loading in general and to study the response of large framed
foundation in particular. The famous example of the large framed machine foundation is
the steam turbine generator foundation. The case study introduced in this thesis is a
HITACHI 650 MW steam turbine generator, this machine is the largest machine operated
in Egypt until now. To model such large framed foundation an ANSYS finite element 3D
model is build using tetrahedral solid elements. The main analyses performed are: (1)
Frequency analysis, (2) harmonic analysis.
Frequency analysis is performed to determine the natural frequency of the foundation and
the percentage of masses captured by the modes of vibration and the frequencies
corresponding to it. In addition to that, the frequency analysis is used in this study to
insure that the foundation natural frequency is outside the machine operating frequency
with +/- 20% margin.
Harmonic analysis is performed to determine the response of the foundation to the
dynamic unbalanced loads that applied from the machine to the foundation during the
machine operation.
The main aim of this thesis is to study the effect of changing damping ratios (2% to 5%),
mesh size (500 mm, 800 mm and 1100 mm), and element types (8-nodded element, 10nodded element and 20-nodded element) on the response of foundation after performing
the frequency and harmonic analysis. Also a seismic check is performed to determine the
97
foundation response to application of seismic forces using two approaches : (1) by
applying the seismic force at the machine anchorage locations, (2) by Applying the
seismic force at the center of gravity of the machine. In addition, concrete with different
compressive strength is examined to determine the response of the structure under
harmonic excitation with respect to the change in the compressive strength of the
concrete.
5.2 Conclusion
Frequency Analysis: The change in the damping ratio has no effect on the fundamental
frequency, for the other parameters, changes in the natural frequency values are observed
due to the changes in the mesh size and element type. For mesh sizes (500 mm to 1100
mm) the fundamental frequency values increase by 1% to 2% for the 8 nodded elements
and 0.4% to 0.6% for the 10 & 20 nodded elements. These changes are not significant,
but it can give a direction that mesh size & element type have no real tangible effect on
the results obtained from this analysis. Based on this result, less complex finite element
model could be used in such type of analysis without significant change on the results.
Harmonic Analysis: The changes in the transverse and vertical response (deflection)
values reflect the change in damping ratio, mesh size, and element type. For the same
mesh size & element type, the increase in the damping ratios from 2% to 5% results in
decreasing the horizontal displacement by a range from 10% to 15% while the vertical
displacement decreases by a bigger range from 16% to 32%. Also for the damping ratios
(2% to 5%) and mesh sizes (500 mm to 1100 mm) the vertical and horizontal
displacements have the same values for the 10-nodded & 20-nodded elements. While for
the damping ratios (2% to 5%) and mesh sizes (500 mm to 1100 mm) the vertical and
horizontal displacements for the 8-nodded elements are 2% to 20% less than the values of
98
10 & 20 nodded elements. Finally it is concluded that the damping ratio has a significant
effect on the structure response in the harmonic analysis of the foundation, Also for the
10-nodded & 20-nodded elements, no significant change in the structure response
observed when the damping ratio or the mesh size have changed, which is not the case
with the 8-nodded element. This could help in using the 10-nodded element in such
analysis type to save time in the analysis and calculation.
The difference in response due to the changes in the compressive strength is minor and
this can be justified by the fact that the deflection is affected by the applied force and the
stiffness. The case here that the stiffness is only influenced by changing the elastic
modulus of concrete (E). The difference in deflection to be significant, the change in the
elastic modulus should be significant, also the inertia (I) and the length (L) of the
structural element are also have an influence on the stiffness, so in order to make tangible
changes in the stiffness, both the inertia and the length of the structural elements should be
changed and this doesn't considered in the case here, so the change in deflection was
minor.
Seismic Analysis: The deflection results from applying seismic force at the machine sole
plates is about 2% more than the deflection results from applying seismic force at the
center of gravity of the machine. This is due to the small distance between the foundation
tabletop and the machine as the center of gravity of the machine is located 900 mm above
the foundation elevation.
99
List of
References
[1] ACI 351.3R-04, Foundations for Dynamic Equipment, American Concrete Institute,
Farmington Hills, Michigan, 2004.
[2] Adhhikari Sukanta, Turbo-Generator Foundation, Structural Engineering Forum of
India, 2010
[3] Ali Ossama, Effective Modeling of Mass Concrete Foundation Under Dynamic
Loads, Master Thesis, The American University in Cairo, 2006
[4] ANSYS user manual, Release 11.0 Documentation of ANSYS, 2007
[5] Arya C. Suresh, O’Neill W. Michael, Pincus George, Design of Structures and
Foundations for Vibrating Machines, Gulf publishing Company, London, 1984.
[6] Bechtel Power Corporation, Geotechnical & Hydraulic Engineering services,
onshore subsurface investigation & foundation report for ELSOKHNA Power plant,
2009.
[7] Bowles, J.E. Foundation Analysis and Design, 3rd Edition, McGraw-Hill Book Co.,
New York, 816 p, 1982.
[8] Chopra K. Anil, Dynamics of Structures, Earthquake Engineering Research
100
Institute, Berkeley, California, 1980.
[9 Chowdhury Indrajit, Dasguptu P. Shambhu , Dynamics of Structure and foundation –
A Unified Approach, Taylor & Francis Group, London, UK, 2009.
[10] DIN 4024, Part 1, Machine Foundations, Flexible structures that support machines
with rotating element, April 1988.
[11] DIN 4024, Part 2, Machine Foundations, Rigid foundations for machinery subject
to periodic vibration , April 1988.
[12] Fleischer, Trombik P. G., Turbo Generator Machine Foundations Subjected to
Earthquake Loadings, The 14th World Conference on Earthquake Engineering, Beijing,
China, 2008.
[13] Fossil Power Committee, Nuclear Power Committee, Energy Division, Design of
Large steam Turbine-Generator Foundations, American Society of Civil Engineers, New
York, 1987.
[14] Gazetas George, Analysis of machine foundation vibrations: State of the art,
International Conference on Soil Dynamics and Earthquake Engineering, England,
1982
[15] Gu Ping, New dynamic participation factor for turbine generator foundation,
American Society of Civil Engineers, 2009.
101
[16] Hadjian H. Asadour, Design Criteria for Turbine-Generator Pedestals, Journal of the
Power Division, Vol. 96, No. 1, January 1970
[17] HITACHI, Turbine and Generator Foundation Design and construction &
recommendation, Tokyo, Japan, 2009.
[18] Karthigeyan V., Prakhya, G. K. V. & Vekaria, K., Dynamic Analysis of a Steam
Turbine Support Structure, Eighth International Conference on Civil & Structural
Engineering Computing; Vienna; Austria; 19-21 Sept. 2001.
[19] Lakshmanan N. & Gopalacrishnan N., New Design Approach for Computing Peak
Dynamic Response of Turbo Generator Pedestals Using Modal Synthesis, ASCE, 2006
[20] Livshits Arkady, Dynamic Analysis and Structural Design of Turbine Generator
Foundations, European Built Environment CAE Conference, London, UK, 2008
[21] Liu, W. and Novak, M., Dynamic behaviour of turbine-generator-foundation
systems. Earthquake Engineering & Structural Dynamics, ch. 24 p.339–360, 2006
[22] Nawrotzki Peter, Huffmann G., Uzunoglo T., Static and Dynamic Analysis
of Concrete Turbine Foundations, Structural Engineering International, March,
2008.
102
[23] Paz Mario, William Leigh, Structural Dynamics: Theory and computation, Kluwer
Academic Publishers, Fourth edition, 2003.
[24] Prakash, S. and V.K. Puri. Foundations for Machines: Analysis and
Design, John Wiley & Sons, Inc., New York, NY, 1988.
[25] Prakash Shamsher, Puri K. Vijay, Foundation for Vibrating Machines, The Journal
of Structural Engineering, SERC, Madras, India, 2006
[26] Ravishankar C., Channakeshava C., Kumar Sreehari B., Design of TurboGenerator Foundations, The 12th International Conference of International Association
for Computer Methods and advances in Geomechanics, Goa, India, 2008.
[27] R.J. Lee, H.Y. Joe, An Evaluation Method of Vibration Severity of Rotating
Machines Under Earthquake Loading, The 14th International Conference on Structural
Mechanics in Reactor Technology, Lyon, France, 1997
[28] Sienkiewicz Z. & Wilczyński B., Minimum‐ Weight Design of
Machine
Foundation under Vertical Load, ASCE, 1993
[29] Tedesco W. Joseph, Mcdougal G. William, Ros C. Allen , Structural Dynamics
Theory and Application, Addison-Wesley, New York, 1st Edition, 1998.
103
APPENDIX (A)
HARMONIC ANALYSIS RESULTS
A-1
Damping 2%:
Mesh Size 500mm – 8-Nodded Element
MAX(Y) = 0.012mm
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX(Z) = 0.01133mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
Frequency
A-2
52
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Damping 2%:
Mesh Size 800mm – 8-Nodded Element
MAX(Y) = 0.00956mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX(Z) = 0.00893mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-3
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 2%:
Mesh Size 1100mm – 8-Nodded Element
MAX(Y) = 0.00926mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX(Z) = 0.00897mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-4
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 2%:
Mesh Size 500mm – 10-Nodded Element
MAX(Y) = 0.01194mm
Transverse Y-Dir
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX(Z) = 0.01034mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-5
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 2%:
Mesh Size 800mm – 10-Nodded Element
MAX(Y) = 0.01094mm
Transverse Y-Dir
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX(Z) = 0.01006mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-6
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 2%:
Mesh Size 1100mm – 10-Nodded Element
MAX(Y) = 0.01139mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.01131mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-7
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Damping 2%:
Mesh Size 500mm –20-Nodded Element
MAX(Y) = 0.01033mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.01034mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-8
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Damping 2%:
Mesh Size 800mm – 20-nodded element
MAX(Y) = 0.01094mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.01006mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48 50 52
Frequency
A-9
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 2%:
Mesh Size 1100mm –20-Nodded Element
MAX(Y) = 0.01139mm
Transverse Y-Dir
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.01131mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-10
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 500mm – 8-Nodded Element
MAX(Y) = 0.00918mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
Frequency
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00879mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-11
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 500mm – 8-Nodded Element
MAX(Y) = 0.00918mm
Transverse Y-Dir
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.00879mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-12
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Damping 3%:
Mesh Size 800mm – 8-Nodded Element
MAX(Y) = 0.00788mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
Frequency
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00761mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-13
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 1100mm – 8-Nodded Element
MAX(Y) = 0.00713mm
Transverse Y-Dir
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.00714mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-14
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 500mm – 10-Nodded Element
MAX(Y) = 0.00903mm
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.00817mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-15
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 800mm – 10-Nodded Element
MAX(Y) = 0.00869mm
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.00851mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-16
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 1100mm – 10-Nodded Element
MAX(Y) = 0.00907mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00896mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48 50 52
Frequency
A-17
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 500mm –20-Nodded Element
MAX(Y) = 0.00903mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00817mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-18
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 800mm –20-Nodded Element
MAX(Y) = 0.00869mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00851mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-19
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 3%:
Mesh Size 1100mm –20-Nodded Element
MAX(Y) = 0.00908mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00896mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-20
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 500mm –8-Nodded Element
MAX(Y) = 0.00756mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00730mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-21
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 800mm – 8-Nodded Element
MAX(Y) = 0.00676mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00662mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-22
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 1100mm – 8-Nodded Element
MAX(Y) = 0.00609mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00610mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-23
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 500mm – 10-Nodded Element
MAX(Y) = 0.00751mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00698mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-24
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 800mm – 10-Nodded Element
MAX(Y) = 0.00743mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00737mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-25
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 1100mm – 10-Nodded Element
MAX(Y) = 0.00765mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00752mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-26
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 500mm –20-Nodded Element
MAX(Y) = 0.00751mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00698mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-27
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 800mm –20-Nodded Element
MAX(Y) = 0.00743mm
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
MAX (Z) = 0.00737mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-28
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 4%:
Mesh Size 1100mm –20-Nodded Element
MAX(Y) = 0.00765mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00752mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-29
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 500mm –8-Nodded Element
MAX(Y) = 0.00652mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00633mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-30
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 800mm –8-Nodded Element
MAX(Y) = 0.00596mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00589mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-31
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 1100mm – 8-Nodded Element
MAX(Y) = 0.00538mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00537mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-32
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 500mm –10-Nodded Element
MAX(Y) = 0.00655mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00635mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-33
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 800mm –10-Nodded Element
MAX(Y) = 0.00659mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00653mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-34
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 1100mm –10-Nodded Element
MAX(Y) = 0.00668mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00655mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-35
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 500mm –20-Nodded Element
MAX(Y) = 0.00655mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00635mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-36
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 800mm –20-Nodded Element
MAX(Y) = 0.00659mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00653mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-37
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
Damping 5%:
Mesh Size 1100mm – 20-Nodded Element
MAX(Y) = 0.00668mm
Transverse Y-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
54
56
58
60
Frequency
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
hitachi
MAX (Z) = 0.00655mm
Vertical Z-Dir
0.02500
Disp. ( mm )
0.02000
0.01500
0.01000
0.00500
0.00000
40
42
44
46
48
50
52
Frequency
A-38
54
56
58
60
Sol-1
Sol-3-4
Sol-5
Sol-6
Sol-7a
Sol-7b
Sol-8a
Sol-8b
Sol-9
Sol-10
Sol-36-3
Sol-11
Sol-12
Sol-13a
Sol-13b
Sol-14a
Sol-14b
Sol-15
Sol-16
Sol-17
Sol-18
Sol-19
Sol-20
Sol-21
Sol-22
Sol-23
Sol-24
Sol-25
Hitachi
APPENDIX (B)
MODAL ANALYSIS RESULTS
B-1
Damping 2%:
Mesh Size 500mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.263
3.348
3.560
7.114
7.355
8.627
10.740
12.604
14.335
14.567
16.915
17.328
18.587
18.777
19.115
20.339
21.179
22.252
22.916
23.471
23.693
23.972
25.038
25.809
25.903
26.318
27.981
28.458
28.621
28.884
29.288
30.068
30.181
30.763
31.420
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
31.962
32.937
33.364
34.442
34.932
35.386
35.744
36.055
37.461
37.872
38.973
39.204
40.076
40.218
40.946
41.431
42.454
42.940
43.194
43.529
43.791
44.858
44.906
46.111
46.272
46.286
46.638
46.871
47.187
47.593
48.424
48.902
49.429
49.953
51.018
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-2
Freq
(Hz)
51.401
52.245
52.360
52.498
52.911
53.459
53.766
53.958
54.542
55.325
55.816
56.241
56.481
56.964
57.185
57.517
57.955
58.444
58.732
59.122
59.752
60.182
60.675
61.290
61.983
62.339
62.857
63.132
63.687
63.949
64.245
64.803
65.135
65.318
66.145
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
66.837
66.875
67.726
67.975
68.493
68.960
69.294
69.428
70.000
70.523
70.779
70.833
70.978
71.315
71.575
71.728
72.149
72.237
72.322
72.479
73.167
73.354
73.553
73.932
73.995
74.349
74.520
74.989
75.416
75.487
75.871
75.984
76.272
76.580
76.777
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.58E-04
2.36E-04
7.35E-10
5.99E-04
4.35E-03
3.56E-03
2.33E-03
4.22E-03
11.9331
0.489402
1.96E-03
1.10E-03
0.106115
4.95E-02
7.57E-02
5.19E-03
4.87E-03
3.12E-03
2.96E-02
1.57E-02
5.49E-02
0.39668
0.231191
8.19E-03
1.68E-03
5.97E-03
8.36E-03
1.82E-02
1.85E-04
0.196538
4.29E-03
1.22E-02
4.12E-02
4.46E-02
4.13E-02
8.45E-02
7.54E-03
2.92E-04
1.01E-02
1.36E-04
1.39E+01
98%
UY
2.38E-02
12.8363
0.335974
0.525275
6.17E-02
0.310454
7.05E-05
1.72E-04
5.66E-06
1.31E-07
2.60E-07
9.97E-07
4.02E-05
3.23E-05
3.98E-06
4.53E-05
1.75E-04
1.69E-06
3.28E-06
5.85E-06
2.46E-05
1.08E-05
1.83E-09
1.59E-04
5.36E-05
1.90E-06
4.56E-04
4.47E-05
4.26E-05
1.67E-05
1.79E-06
3.15E-05
1.88E-10
5.77E-05
7.17E-07
4.22E-07
4.84E-05
3.10E-06
2.03E-05
6.78E-06
1.41E+01
99%
UX
1.28E+01
1.57E-02
4.35E-02
7.71E-02
1.11036
6.27E-03
1.50E-05
1.88E-06
1.71E-05
2.21E-04
5.88E-05
6.80E-08
2.49E-05
2.57E-05
3.34E-04
1.95E-06
8.47E-07
7.86E-07
4.96E-07
9.83E-07
3.77E-05
1.56E-04
7.98E-05
2.22E-07
3.08E-05
5.83E-06
9.95E-06
7.94E-05
4.74E-07
1.50E-05
1.12E-05
1.34E-05
7.16E-06
1.01E-06
8.00E-05
1.18E-05
6.96E-05
2.69E-05
5.04E-06
1.47E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
B-3
Damping 2%:
Mesh Size 800mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.344
3.395
3.629
7.513
7.784
8.989
11.335
13.667
14.693
15.021
17.523
18.295
19.039
19.586
19.992
21.107
22.263
23.317
24.024
24.646
24.926
26.032
26.592
26.844
27.259
27.298
29.243
29.600
29.853
30.097
31.241
31.485
31.846
32.079
33.134
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
33.770
34.367
34.737
36.213
36.646
37.314
37.422
37.803
39.049
39.376
40.630
40.870
41.379
41.981
42.744
42.952
44.098
44.316
44.696
45.093
45.862
46.008
46.862
47.436
47.571
48.134
48.657
48.775
49.200
49.271
49.605
49.932
50.347
51.753
51.930
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-4
Freq
(Hz)
52.394
52.816
53.646
54.479
54.876
55.149
55.960
56.208
56.889
57.464
57.792
57.880
58.646
58.948
59.216
59.283
59.737
60.737
61.026
61.354
61.922
62.341
62.523
62.894
63.013
64.036
64.234
64.794
65.079
65.303
65.440
65.704
66.210
66.709
67.164
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
67.512
68.206
68.382
68.697
69.055
69.541
70.304
70.892
70.968
71.525
71.972
72.403
72.642
73.014
73.119
73.526
73.719
73.941
74.137
74.396
74.453
74.648
74.949
75.104
75.303
76.005
76.413
76.761
76.904
77.248
77.500
77.879
78.290
78.527
78.617
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.37E-04
2.04E-04
7.61E-07
1.15E-03
4.80E-03
3.51E-03
2.33E-03
1.43E-02
1.25E+01
8.17E-02
2.79E-03
7.22E-04
4.76E-03
7.61E-02
7.63E-02
4.03E-03
5.33E-03
1.37E-02
4.47E-02
1.02E-01
2.38E-01
2.63E-01
9.41E-03
2.07E-02
8.19E-03
3.01E-05
7.38E-03
8.69E-02
4.93E-04
1.30E-01
6.24E-02
9.51E-05
1.03E-02
4.87E-02
7.88E-02
5.35E-04
1.39E-04
8.21E-03
1.84E-02
8.50E-03
1.39E+01
98%
UY
6.33E-02
1.32E+01
9.89E-02
4.86E-01
3.50E-02
2.28E-01
1.27E-06
6.94E-05
5.62E-06
1.67E-07
1.55E-07
1.25E-05
5.62E-05
8.50E-07
9.40E-07
3.19E-05
1.41E-04
7.73E-07
1.40E-05
1.98E-05
2.49E-05
6.39E-06
2.53E-05
2.41E-05
8.31E-05
3.09E-05
3.55E-04
1.73E-05
2.23E-05
1.79E-05
1.42E-05
1.46E-06
7.64E-05
3.80E-06
4.46E-07
7.24E-06
7.09E-06
5.02E-05
6.45E-06
3.43E-05
1.41E+01
99%
UX
1.31E+01
5.33E-02
7.51E-02
3.03E-02
8.65E-01
6.29E-03
7.92E-06
1.55E-06
3.03E-05
1.17E-04
6.26E-05
6.93E-07
1.23E-05
1.53E-05
3.00E-04
3.16E-06
1.32E-06
4.11E-06
6.36E-06
6.34E-05
7.46E-05
1.93E-05
1.73E-05
8.22E-06
1.81E-05
1.63E-07
8.46E-06
2.07E-05
2.47E-06
1.64E-05
2.33E-05
5.96E-06
2.08E-05
1.41E-05
2.73E-07
6.24E-05
8.41E-05
1.06E-06
2.08E-05
3.02E-10
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
B-5
Damping 2%:
Mesh Size 1100mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.397
3.420
3.666
7.734
8.125
9.246
11.817
14.496
14.951
15.336
18.024
18.942
19.591
20.255
20.819
21.744
23.237
24.191
25.017
25.467
26.122
27.041
27.772
28.161
28.392
28.799
30.621
30.776
31.330
31.539
32.817
32.875
33.206
33.559
34.377
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
35.388
35.937
36.464
37.953
38.501
38.946
39.375
39.828
41.158
41.458
42.614
43.131
43.792
44.394
44.877
45.193
46.044
46.198
46.461
46.860
47.989
48.515
48.966
49.929
49.950
50.248
50.646
50.716
51.011
51.315
51.445
51.747
52.581
53.236
54.046
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-6
Freq
(Hz)
54.905
54.948
55.912
56.330
56.726
57.281
58.212
58.830
59.406
59.675
60.490
60.853
60.942
61.352
61.895
62.231
62.673
62.996
63.359
64.106
64.249
64.820
64.998
65.041
65.192
65.693
66.155
66.818
67.147
67.688
67.947
68.319
68.463
68.817
69.527
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
69.745
70.029
70.671
70.853
71.636
72.254
72.537
73.108
73.243
73.379
73.715
73.942
74.325
74.438
74.646
74.929
75.177
75.424
75.793
75.981
76.270
76.508
76.669
76.960
77.292
77.484
77.773
78.269
79.169
79.382
79.729
79.831
79.972
80.222
80.483
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.27E-04
1.80E-04
2.12E-06
1.78E-03
4.87E-03
3.34E-03
2.60E-03
8.91E-02
1.25E+01
1.23E-01
3.25E-03
8.25E-04
4.48E-04
4.73E-02
7.21E-02
5.14E-03
5.24E-03
1.64E-02
4.89E-04
1.75E-01
2.75E-01
1.68E-01
1.29E-02
8.36E-03
1.83E-03
2.49E-02
7.04E-03
9.48E-02
7.07E-02
3.48E-02
3.89E-02
6.81E-03
4.60E-02
9.91E-03
5.60E-02
6.87E-05
2.22E-04
1.06E-02
3.44E-02
1.44E-04
1.40E+01
98%
UY
0.169179
13.1976
5.43E-02
0.466307
1.74E-02
0.189501
3.08E-07
4.60E-05
7.01E-06
2.66E-07
3.64E-08
3.72E-05
2.58E-05
1.24E-07
6.46E-07
3.72E-05
8.82E-05
4.41E-07
1.18E-05
2.58E-05
2.13E-05
3.92E-06
3.65E-05
9.12E-06
6.39E-06
8.09E-05
1.96E-04
6.45E-07
2.87E-05
8.52E-05
6.72E-07
7.77E-06
2.95E-05
4.21E-05
4.08E-06
1.49E-06
9.26E-06
3.31E-05
1.33E-05
1.19E-05
1.41E+01
99%
UX
1.31E+01
1.53E-01
1.10E-01
9.34E-03
7.13E-01
5.99E-03
5.28E-06
2.04E-06
2.51E-05
6.50E-05
5.37E-05
2.98E-06
5.42E-06
3.02E-05
2.37E-04
5.16E-06
1.30E-06
3.60E-06
2.91E-05
4.63E-05
3.16E-05
4.13E-05
1.41E-05
1.14E-06
3.50E-07
3.35E-06
5.68E-06
5.57E-06
3.17E-06
5.30E-06
7.99E-09
3.08E-05
3.00E-06
1.08E-05
2.72E-07
1.36E-05
1.14E-04
1.58E-06
2.16E-05
4.81E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.397
2
3.420
3
3.666
4
7.734
5
8.125
6
9.246
7
11.817
8
14.496
9
14.951
10
15.336
11
18.024
12
18.942
13
19.591
14
20.255
15
20.819
16
21.744
17
23.237
18
24.191
19
25.017
20
25.467
21
26.122
22
27.041
23
27.772
24
28.161
25
28.392
26
28.799
27
30.621
28
30.776
29
31.330
30
31.539
31
32.817
32
32.875
33
33.206
34
33.559
35
34.377
36
35.388
37
35.937
38
36.464
39
37.953
40
38.501
SUM
Sum / Total mass
B-7
Damping 2%:
Mesh Size 500mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.733
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-8
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.265
58.431
59.028
59.185
59.557
59.714
60.251
60.744
61.274
61.460
62.329
62.813
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.626
65.592
66.000
66.166
66.601
66.988
67.168
67.513
67.949
68.570
68.744
68.941
69.150
69.421
69.452
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.665
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.77E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
1.24E+01
1.73E-02
1.67E-02
1.11E-01
1.50E+00
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-9
Damping 2%:
Mesh Size 800mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.276
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.922
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.171
40.131
40.891
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.070
45.535
46.030
46.194
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-10
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.182
51.806
52.019
52.589
52.722
53.246
53.540
53.993
54.606
55.167
55.538
56.275
56.385
56.460
56.779
57.087
57.675
57.888
58.653
58.815
59.480
59.641
60.045
60.288
60.766
61.266
61.898
61.991
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.826
64.394
64.904
65.244
66.001
66.506
66.755
67.113
67.476
67.692
68.123
68.442
69.204
69.375
69.741
70.110
70.218
70.423
70.519
70.902
71.168
71.403
71.467
71.709
72.216
72.436
72.580
73.044
73.446
73.971
74.215
74.440
74.629
75.092
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.02E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.21E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405502
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.05E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.71E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.18E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
1.25E+01
1.33E-02
1.94E-02
1.03E-01
1.46E+00
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.25E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.276
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-11
Damping 2%:
Mesh Size 1100mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.529
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.699
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.539
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.795
38.670
38.749
39.384
39.462
40.399
41.111
41.212
42.170
42.533
43.088
43.694
44.126
44.246
44.472
45.125
45.346
45.783
46.279
46.464
47.802
48.106
48.718
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-12
Freq
(Hz)
49.202
49.298
49.836
50.656
50.876
51.554
52.125
52.322
52.892
53.054
53.567
53.886
54.304
54.950
55.639
55.985
56.656
56.755
56.793
57.123
57.543
58.097
58.338
59.117
59.224
59.876
60.095
60.488
60.800
61.289
61.750
62.325
62.541
63.456
63.852
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.952
64.385
65.002
65.396
65.765
66.417
66.993
67.221
67.646
68.004
68.226
68.680
68.969
69.782
69.820
70.319
70.746
70.803
71.125
71.191
71.485
71.741
71.923
71.963
72.251
72.934
73.044
73.179
73.759
74.173
74.637
74.875
75.234
75.306
75.665
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.11E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393026
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.20E-05
8.91E-07
5.12E-04
6.29E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
1.25E+01
1.06E-02
2.17E-02
1.02E-01
1.42E+00
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.529
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.699
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.539
39
32.862
40
33.441
SUM
Sum / Total mass
B-13
Damping 2%:
Mesh Size 500mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.734
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-14
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.266
58.431
59.028
59.185
59.557
59.715
60.251
60.744
61.274
61.460
62.329
62.814
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.627
65.592
66.000
66.166
66.601
66.988
67.169
67.513
67.949
68.571
68.744
68.941
69.150
69.421
69.453
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.666
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.76E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
1.24E+01
1.73E-02
1.67E-02
1.11E-01
1.50E+00
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-15
Damping 2%:
Mesh Size 800mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.277
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.923
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.172
40.131
40.892
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.071
45.535
46.030
46.195
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-16
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.183
51.806
52.020
52.589
52.722
53.246
53.540
53.993
54.606
55.168
55.538
56.275
56.385
56.460
56.779
57.088
57.676
57.889
58.653
58.815
59.481
59.641
60.045
60.289
60.767
61.267
61.899
61.992
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.827
64.394
64.904
65.244
66.002
66.506
66.756
67.114
67.477
67.693
68.124
68.443
69.205
69.376
69.742
70.111
70.219
70.424
70.519
70.902
71.169
71.404
71.468
71.710
72.217
72.436
72.581
73.044
73.447
73.971
74.216
74.441
74.630
75.093
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.01E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.22E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405501
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.06E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.70E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.17E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
1.25E+01
1.33E-02
1.94E-02
1.03E-01
1.46E+00
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.26E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.277
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-17
Damping 2%:
Mesh Size 1100mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.530
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.700
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.540
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.796
38.671
38.749
39.385
39.462
40.399
41.112
41.212
42.170
42.534
43.089
43.694
44.127
44.247
44.473
45.125
45.346
45.784
46.280
46.465
47.803
48.106
48.719
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-18
Freq
(Hz)
49.202
49.298
49.837
50.657
50.877
51.555
52.126
52.323
52.893
53.055
53.568
53.887
54.305
54.951
55.640
55.986
56.657
56.756
56.793
57.124
57.544
58.098
58.339
59.118
59.226
59.877
60.096
60.489
60.802
61.291
61.752
62.327
62.543
63.457
63.853
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.953
64.386
65.004
65.397
65.767
66.419
66.995
67.222
67.648
68.006
68.228
68.682
68.972
69.785
69.822
70.320
70.748
70.805
71.126
71.192
71.487
71.743
71.925
71.965
72.253
72.936
73.046
73.181
73.761
74.175
74.639
74.878
75.236
75.309
75.667
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.12E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393025
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.21E-05
8.92E-07
5.12E-04
6.18E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
1.25E+01
1.06E-02
2.17E-02
1.02E-01
1.42E+00
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.530
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.700
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.540
39
32.862
40
33.441
SUM
Sum / Total mass
B-19
Damping 3%:
Mesh Size 500mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.263
3.348
3.560
7.114
7.355
8.627
10.740
12.604
14.335
14.567
16.915
17.328
18.587
18.777
19.115
20.339
21.179
22.252
22.916
23.471
23.693
23.972
25.038
25.809
25.903
26.318
27.981
28.458
28.621
28.884
29.288
30.068
30.181
30.763
31.420
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
31.962
32.937
33.364
34.442
34.932
35.386
35.744
36.055
37.461
37.872
38.973
39.204
40.076
40.218
40.946
41.431
42.454
42.940
43.194
43.529
43.791
44.858
44.906
46.111
46.272
46.286
46.638
46.871
47.187
47.593
48.424
48.902
49.429
49.953
51.018
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-20
Freq
(Hz)
51.401
52.245
52.360
52.498
52.911
53.459
53.766
53.958
54.542
55.325
55.816
56.241
56.481
56.964
57.185
57.517
57.955
58.444
58.732
59.122
59.752
60.182
60.675
61.290
61.983
62.339
62.857
63.132
63.687
63.949
64.245
64.803
65.135
65.318
66.145
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
66.837
66.875
67.726
67.975
68.493
68.960
69.294
69.428
70.000
70.523
70.779
70.833
70.978
71.315
71.575
71.728
72.149
72.237
72.322
72.479
73.167
73.354
73.553
73.932
73.995
74.349
74.520
74.989
75.416
75.487
75.871
75.984
76.272
76.580
76.777
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.58E-04
2.36E-04
7.35E-10
5.99E-04
4.35E-03
3.56E-03
2.33E-03
4.22E-03
1.19E+01
4.89E-01
1.96E-03
1.10E-03
1.06E-01
4.95E-02
7.57E-02
5.19E-03
4.87E-03
3.12E-03
2.96E-02
1.57E-02
5.49E-02
3.97E-01
2.31E-01
8.19E-03
1.68E-03
5.97E-03
8.36E-03
1.82E-02
1.85E-04
1.97E-01
4.29E-03
1.22E-02
4.12E-02
4.46E-02
4.13E-02
8.45E-02
7.54E-03
2.92E-04
1.01E-02
1.36E-04
1.39E+01
98%
UY
0.0238171
12.8363
3.36E-01
0.525275
6.17E-02
0.310454
7.05E-05
1.72E-04
5.66E-06
1.31E-07
2.60E-07
9.97E-07
4.02E-05
3.23E-05
3.98E-06
4.53E-05
1.75E-04
1.69E-06
3.28E-06
5.85E-06
2.46E-05
1.08E-05
1.83E-09
1.59E-04
5.36E-05
1.90E-06
4.56E-04
4.47E-05
4.26E-05
1.67E-05
1.79E-06
3.15E-05
1.88E-10
5.77E-05
7.17E-07
4.22E-07
4.84E-05
3.10E-06
2.03E-05
6.78E-06
1.41E+01
99%
UX
1.28E+01
1.57E-02
4.35E-02
7.71E-02
1.11E+00
6.27E-03
1.50E-05
1.88E-06
1.71E-05
2.21E-04
5.88E-05
6.80E-08
2.49E-05
2.57E-05
3.34E-04
1.95E-06
8.47E-07
7.86E-07
4.96E-07
9.83E-07
3.77E-05
1.56E-04
7.98E-05
2.22E-07
3.08E-05
5.83E-06
9.95E-06
7.94E-05
4.74E-07
1.50E-05
1.12E-05
1.34E-05
7.16E-06
1.01E-06
8.00E-05
1.18E-05
6.96E-05
2.69E-05
5.04E-06
1.47E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
B-21
Damping 3%:
Mesh Size 800mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.344
3.395
3.629
7.513
7.784
8.989
11.335
13.667
14.693
15.021
17.523
18.295
19.039
19.586
19.992
21.107
22.263
23.317
24.024
24.646
24.926
26.032
26.592
26.844
27.259
27.298
29.243
29.600
29.853
30.097
31.241
31.485
31.846
32.079
33.134
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
33.770
34.367
34.737
36.213
36.646
37.314
37.422
37.803
39.049
39.376
40.630
40.870
41.379
41.981
42.744
42.952
44.098
44.316
44.696
45.093
45.862
46.008
46.862
47.436
47.571
48.134
48.657
48.775
49.200
49.271
49.605
49.932
50.347
51.753
51.930
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-22
Freq
(Hz)
52.394
52.816
53.646
54.479
54.876
55.149
55.960
56.208
56.889
57.464
57.792
57.880
58.646
58.948
59.216
59.283
59.737
60.737
61.026
61.354
61.922
62.341
62.523
62.894
63.013
64.036
64.234
64.794
65.079
65.303
65.440
65.704
66.210
66.709
67.164
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
67.512
68.206
68.382
68.697
69.055
69.541
70.304
70.892
70.968
71.525
71.972
72.403
72.642
73.014
73.119
73.526
73.719
73.941
74.137
74.396
74.453
74.648
74.949
75.104
75.303
76.005
76.413
76.761
76.904
77.248
77.500
77.879
78.290
78.527
78.617
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.37E-04
2.04E-04
7.61E-07
1.15E-03
4.80E-03
3.51E-03
2.33E-03
1.43E-02
1.25E+01
8.17E-02
2.79E-03
7.22E-04
4.76E-03
7.61E-02
7.63E-02
4.03E-03
5.33E-03
1.37E-02
4.47E-02
1.02E-01
2.38E-01
2.63E-01
9.41E-03
2.07E-02
8.19E-03
3.01E-05
7.38E-03
8.69E-02
4.93E-04
1.30E-01
6.24E-02
9.51E-05
1.03E-02
4.87E-02
7.88E-02
5.35E-04
1.39E-04
8.21E-03
1.84E-02
8.50E-03
1.39E+01
98%
UY
0.0633402
13.183
9.89E-02
0.485796
3.50E-02
0.227832
1.27E-06
6.94E-05
5.62E-06
1.67E-07
1.55E-07
1.25E-05
5.62E-05
8.50E-07
9.40E-07
3.19E-05
1.41E-04
7.73E-07
1.40E-05
1.98E-05
2.49E-05
6.39E-06
2.53E-05
2.41E-05
8.31E-05
3.09E-05
3.55E-04
1.73E-05
2.23E-05
1.79E-05
1.42E-05
1.46E-06
7.64E-05
3.80E-06
4.46E-07
7.24E-06
7.09E-06
5.02E-05
6.45E-06
3.43E-05
1.41E+01
99%
UX
1.31E+01
5.33E-02
7.51E-02
3.03E-02
8.65E-01
6.29E-03
7.92E-06
1.55E-06
3.03E-05
1.17E-04
6.26E-05
6.93E-07
1.23E-05
1.53E-05
3.00E-04
3.16E-06
1.32E-06
4.11E-06
6.36E-06
6.34E-05
7.46E-05
1.93E-05
1.73E-05
8.22E-06
1.81E-05
1.63E-07
8.46E-06
2.07E-05
2.47E-06
1.64E-05
2.33E-05
5.96E-06
2.08E-05
1.41E-05
2.73E-07
6.24E-05
8.41E-05
1.06E-06
2.08E-05
3.02E-10
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.344
2
3.395
3
3.629
4
7.513
5
7.784
6
8.989
7
11.335
8
13.667
9
14.693
10
15.021
11
17.523
12
18.295
13
19.039
14
19.586
15
19.992
16
21.107
17
22.263
18
23.317
19
24.024
20
24.646
21
24.926
22
26.032
23
26.592
24
26.844
25
27.259
26
27.298
27
29.243
28
29.600
29
29.853
30
30.097
31
31.241
32
31.485
33
31.846
34
32.079
35
33.134
36
33.770
37
34.367
38
34.737
39
36.213
40
36.646
SUM
Sum / Total mass
B-23
Damping 3%:
Mesh Size 1100mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.397
3.420
3.666
7.734
8.125
9.246
11.817
14.496
14.951
15.336
18.024
18.942
19.591
20.255
20.819
21.744
23.237
24.191
25.017
25.467
26.122
27.041
27.772
28.161
28.392
28.799
30.621
30.776
31.330
31.539
32.817
32.875
33.206
33.559
34.377
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
35.388
35.937
36.464
37.953
38.501
38.946
39.375
39.828
41.158
41.458
42.614
43.131
43.792
44.394
44.877
45.193
46.044
46.198
46.461
46.860
47.989
48.515
48.966
49.929
49.950
50.248
50.646
50.716
51.011
51.315
51.445
51.747
52.581
53.236
54.046
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-24
Freq
(Hz)
54.905
54.948
55.912
56.330
56.726
57.281
58.212
58.830
59.406
59.675
60.490
60.853
60.942
61.352
61.895
62.231
62.673
62.996
63.359
64.106
64.249
64.820
64.998
65.041
65.192
65.693
66.155
66.818
67.147
67.688
67.947
68.319
68.463
68.817
69.527
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
69.745
70.029
70.671
70.853
71.636
72.254
72.537
73.108
73.243
73.379
73.715
73.942
74.325
74.438
74.646
74.929
75.177
75.424
75.793
75.981
76.270
76.508
76.669
76.960
77.292
77.484
77.773
78.269
79.169
79.382
79.729
79.831
79.972
80.222
80.483
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.27E-04
1.80E-04
2.12E-06
1.78E-03
4.87E-03
3.34E-03
2.60E-03
8.91E-02
1.25E+01
1.23E-01
3.25E-03
8.25E-04
4.48E-04
4.73E-02
7.21E-02
5.14E-03
5.24E-03
1.64E-02
4.89E-04
1.75E-01
2.75E-01
1.68E-01
1.29E-02
8.36E-03
1.83E-03
2.49E-02
7.04E-03
9.48E-02
7.07E-02
3.48E-02
3.89E-02
6.81E-03
4.60E-02
9.91E-03
5.60E-02
6.87E-05
2.22E-04
1.06E-02
3.44E-02
1.44E-04
1.40E+01
98%
UY
0.169179
13.1976
5.43E-02
0.466307
1.74E-02
0.189501
3.08E-07
4.60E-05
7.01E-06
2.66E-07
3.64E-08
3.72E-05
2.58E-05
1.24E-07
6.46E-07
3.72E-05
8.82E-05
4.41E-07
1.18E-05
2.58E-05
2.13E-05
3.92E-06
3.65E-05
9.12E-06
6.39E-06
8.09E-05
1.96E-04
6.45E-07
2.87E-05
8.52E-05
6.72E-07
7.77E-06
2.95E-05
4.21E-05
4.08E-06
1.49E-06
9.26E-06
3.31E-05
1.33E-05
1.19E-05
1.41E+01
99%
UX
1.31E+01
1.53E-01
1.10E-01
9.34E-03
7.13E-01
5.99E-03
5.28E-06
2.04E-06
2.51E-05
6.50E-05
5.37E-05
2.98E-06
5.42E-06
3.02E-05
2.37E-04
5.16E-06
1.30E-06
3.60E-06
2.91E-05
4.63E-05
3.16E-05
4.13E-05
1.41E-05
1.14E-06
3.50E-07
3.35E-06
5.68E-06
5.57E-06
3.17E-06
5.30E-06
7.99E-09
3.08E-05
3.00E-06
1.08E-05
2.72E-07
1.36E-05
1.14E-04
1.58E-06
2.16E-05
4.81E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.397
2
3.420
3
3.666
4
7.734
5
8.125
6
9.246
7
11.817
8
14.496
9
14.951
10
15.336
11
18.024
12
18.942
13
19.591
14
20.255
15
20.819
16
21.744
17
23.237
18
24.191
19
25.017
20
25.467
21
26.122
22
27.041
23
27.772
24
28.161
25
28.392
26
28.799
27
30.621
28
30.776
29
31.330
30
31.539
31
32.817
32
32.875
33
33.206
34
33.559
35
34.377
36
35.388
37
35.937
38
36.464
39
37.953
40
38.501
SUM
Sum / Total mass
B-25
Damping 3%:
Mesh Size 500mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.733
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-26
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.265
58.431
59.028
59.185
59.557
59.714
60.251
60.744
61.274
61.460
62.329
62.813
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.626
65.592
66.000
66.166
66.601
66.988
67.168
67.513
67.949
68.570
68.744
68.941
69.150
69.421
69.452
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.665
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.77E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
1.24E+01
1.73E-02
1.67E-02
1.11E-01
1.50E+00
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-27
Damping 3%:
Mesh Size 800mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.276
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.922
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.171
40.131
40.891
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.070
45.535
46.030
46.194
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-28
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.182
51.806
52.019
52.589
52.722
53.246
53.540
53.993
54.606
55.167
55.538
56.275
56.385
56.460
56.779
57.087
57.675
57.888
58.653
58.815
59.480
59.641
60.045
60.288
60.766
61.266
61.898
61.991
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.826
64.394
64.904
65.244
66.001
66.506
66.755
67.113
67.476
67.692
68.123
68.442
69.204
69.375
69.741
70.110
70.218
70.423
70.519
70.902
71.168
71.403
71.467
71.709
72.216
72.436
72.580
73.044
73.446
73.971
74.215
74.440
74.629
75.092
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.02E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.21E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405502
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.05E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.71E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.18E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
1.25E+01
1.33E-02
1.94E-02
1.03E-01
1.46E+00
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.25E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.276
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-29
Damping 3%:
Mesh Size 1100mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.529
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.699
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.539
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.795
38.670
38.749
39.384
39.462
40.399
41.111
41.212
42.170
42.533
43.088
43.694
44.126
44.246
44.472
45.125
45.346
45.783
46.279
46.464
47.802
48.106
48.718
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-30
Freq
(Hz)
49.202
49.298
49.836
50.656
50.876
51.554
52.125
52.322
52.892
53.054
53.567
53.886
54.304
54.950
55.639
55.985
56.656
56.755
56.793
57.123
57.543
58.097
58.338
59.117
59.224
59.876
60.095
60.488
60.800
61.289
61.750
62.325
62.541
63.456
63.852
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.952
64.385
65.002
65.396
65.765
66.417
66.993
67.221
67.646
68.004
68.226
68.680
68.969
69.782
69.820
70.319
70.746
70.803
71.125
71.191
71.485
71.741
71.923
71.963
72.251
72.934
73.044
73.179
73.759
74.173
74.637
74.875
75.234
75.306
75.665
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.11E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393026
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.20E-05
8.91E-07
5.12E-04
6.29E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
1.25E+01
1.06E-02
2.17E-02
1.02E-01
1.42E+00
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.529
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.699
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.539
39
32.862
40
33.441
SUM
Sum / Total mass
B-31
Damping 3%:
Mesh Size 500mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.734
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-32
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.266
58.431
59.028
59.185
59.557
59.715
60.251
60.744
61.274
61.460
62.329
62.814
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.627
65.592
66.000
66.166
66.601
66.988
67.169
67.513
67.949
68.571
68.744
68.941
69.150
69.421
69.453
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.666
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.76E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
12.4382
1.73E-02
1.67E-02
0.111228
1.5018
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-33
Damping 3%:
Mesh Size 800mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.277
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.923
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.172
40.131
40.892
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.071
45.535
46.030
46.195
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-34
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.183
51.806
52.020
52.589
52.722
53.246
53.540
53.993
54.606
55.168
55.538
56.275
56.385
56.460
56.779
57.088
57.676
57.889
58.653
58.815
59.481
59.641
60.045
60.289
60.767
61.267
61.899
61.992
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.827
64.394
64.904
65.244
66.002
66.506
66.756
67.114
67.477
67.693
68.124
68.443
69.205
69.376
69.742
70.111
70.219
70.424
70.519
70.902
71.169
71.404
71.468
71.710
72.217
72.436
72.581
73.044
73.447
73.971
74.216
74.441
74.630
75.093
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.01E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.22E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405501
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.06E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.70E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.17E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
12.4882
1.33E-02
1.94E-02
0.10322
1.46233
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.26E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.277
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-35
Damping 3%:
Mesh Size 1100mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.530
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.700
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.540
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.796
38.671
38.749
39.385
39.462
40.399
41.112
41.212
42.170
42.534
43.089
43.694
44.127
44.247
44.473
45.125
45.346
45.784
46.280
46.465
47.803
48.106
48.719
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-36
Freq
(Hz)
49.202
49.298
49.837
50.657
50.877
51.555
52.126
52.323
52.893
53.055
53.568
53.887
54.305
54.951
55.640
55.986
56.657
56.756
56.793
57.124
57.544
58.098
58.339
59.118
59.226
59.877
60.096
60.489
60.802
61.291
61.752
62.327
62.543
63.457
63.853
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.953
64.386
65.004
65.397
65.767
66.419
66.995
67.222
67.648
68.006
68.228
68.682
68.972
69.785
69.822
70.320
70.748
70.805
71.126
71.192
71.487
71.743
71.925
71.965
72.253
72.936
73.046
73.181
73.761
74.175
74.639
74.878
75.236
75.309
75.667
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.12E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393025
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.21E-05
8.92E-07
5.12E-04
6.18E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
12.5305
1.06E-02
2.17E-02
0.101603
1.42252
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.530
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.700
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.540
39
32.862
40
33.441
SUM
Sum / Total mass
B-37
Damping 4%:
Mesh Size 500mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.263
3.348
3.560
7.114
7.355
8.627
10.740
12.604
14.335
14.567
16.915
17.328
18.587
18.777
19.115
20.339
21.179
22.252
22.916
23.471
23.693
23.972
25.038
25.809
25.903
26.318
27.981
28.458
28.621
28.884
29.288
30.068
30.181
30.763
31.420
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
31.962
32.937
33.364
34.442
34.932
35.386
35.744
36.055
37.461
37.872
38.973
39.204
40.076
40.218
40.946
41.431
42.454
42.940
43.194
43.529
43.791
44.858
44.906
46.111
46.272
46.286
46.638
46.871
47.187
47.593
48.424
48.902
49.429
49.953
51.018
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-38
Freq
(Hz)
51.401
52.245
52.360
52.498
52.911
53.459
53.766
53.958
54.542
55.325
55.816
56.241
56.481
56.964
57.185
57.517
57.955
58.444
58.732
59.122
59.752
60.182
60.675
61.290
61.983
62.339
62.857
63.132
63.687
63.949
64.245
64.803
65.135
65.318
66.145
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
66.837
66.875
67.726
67.975
68.493
68.960
69.294
69.428
70.000
70.523
70.779
70.833
70.978
71.315
71.575
71.728
72.149
72.237
72.322
72.479
73.167
73.354
73.553
73.932
73.995
74.349
74.520
74.989
75.416
75.487
75.871
75.984
76.272
76.580
76.777
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.58E-04
2.36E-04
7.35E-10
5.99E-04
4.35E-03
3.56E-03
2.33E-03
4.22E-03
1.19E+01
4.89E-01
1.96E-03
1.10E-03
1.06E-01
4.95E-02
7.57E-02
5.19E-03
4.87E-03
3.12E-03
2.96E-02
1.57E-02
5.49E-02
3.97E-01
2.31E-01
8.19E-03
1.68E-03
5.97E-03
8.36E-03
1.82E-02
1.85E-04
1.97E-01
4.29E-03
1.22E-02
4.12E-02
4.46E-02
4.13E-02
8.45E-02
7.54E-03
2.92E-04
1.01E-02
1.36E-04
1.39E+01
98%
UY
0.0238171
12.8363
3.36E-01
0.525275
6.17E-02
0.310454
7.05E-05
1.72E-04
5.66E-06
1.31E-07
2.60E-07
9.97E-07
4.02E-05
3.23E-05
3.98E-06
4.53E-05
1.75E-04
1.69E-06
3.28E-06
5.85E-06
2.46E-05
1.08E-05
1.83E-09
1.59E-04
5.36E-05
1.90E-06
4.56E-04
4.47E-05
4.26E-05
1.67E-05
1.79E-06
3.15E-05
1.88E-10
5.77E-05
7.17E-07
4.22E-07
4.84E-05
3.10E-06
2.03E-05
6.78E-06
1.41E+01
99%
UX
12.8409
1.57E-02
4.35E-02
0.0771418
1.11036
6.27E-03
1.50E-05
1.88E-06
1.71E-05
2.21E-04
5.88E-05
6.80E-08
2.49E-05
2.57E-05
3.34E-04
1.95E-06
8.47E-07
7.86E-07
4.96E-07
9.83E-07
3.77E-05
1.56E-04
7.98E-05
2.22E-07
3.08E-05
5.83E-06
9.95E-06
7.94E-05
4.74E-07
1.50E-05
1.12E-05
1.34E-05
7.16E-06
1.01E-06
8.00E-05
1.18E-05
6.96E-05
2.69E-05
5.04E-06
1.47E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
B-39
Damping 4%:
Mesh Size 800mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.344
3.395
3.629
7.513
7.784
8.989
11.335
13.667
14.693
15.021
17.523
18.295
19.039
19.586
19.992
21.107
22.263
23.317
24.024
24.646
24.926
26.032
26.592
26.844
27.259
27.298
29.243
29.600
29.853
30.097
31.241
31.485
31.846
32.079
33.134
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
33.770
34.367
34.737
36.213
36.646
37.314
37.422
37.803
39.049
39.376
40.630
40.870
41.379
41.981
42.744
42.952
44.098
44.316
44.696
45.093
45.862
46.008
46.862
47.436
47.571
48.134
48.657
48.775
49.200
49.271
49.605
49.932
50.347
51.753
51.930
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-40
Freq
(Hz)
52.394
52.816
53.646
54.479
54.876
55.149
55.960
56.208
56.889
57.464
57.792
57.880
58.646
58.948
59.216
59.283
59.737
60.737
61.026
61.354
61.922
62.341
62.523
62.894
63.013
64.036
64.234
64.794
65.079
65.303
65.440
65.704
66.210
66.709
67.164
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
67.512
68.206
68.382
68.697
69.055
69.541
70.304
70.892
70.968
71.525
71.972
72.403
72.642
73.014
73.119
73.526
73.719
73.941
74.137
74.396
74.453
74.648
74.949
75.104
75.303
76.005
76.413
76.761
76.904
77.248
77.500
77.879
78.290
78.527
78.617
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.37E-04
2.04E-04
7.61E-07
1.15E-03
4.80E-03
3.51E-03
2.33E-03
1.43E-02
1.25E+01
8.17E-02
2.79E-03
7.22E-04
4.76E-03
7.61E-02
7.63E-02
4.03E-03
5.33E-03
1.37E-02
4.47E-02
1.02E-01
2.38E-01
2.63E-01
9.41E-03
2.07E-02
8.19E-03
3.01E-05
7.38E-03
8.69E-02
4.93E-04
1.30E-01
6.24E-02
9.51E-05
1.03E-02
4.87E-02
7.88E-02
5.35E-04
1.39E-04
8.21E-03
1.84E-02
8.50E-03
1.39E+01
98%
UY
0.0633402
13.183
9.89E-02
0.485796
3.50E-02
0.227832
1.27E-06
6.94E-05
5.62E-06
1.67E-07
1.55E-07
1.25E-05
5.62E-05
8.50E-07
9.40E-07
3.19E-05
1.41E-04
7.73E-07
1.40E-05
1.98E-05
2.49E-05
6.39E-06
2.53E-05
2.41E-05
8.31E-05
3.09E-05
3.55E-04
1.73E-05
2.23E-05
1.79E-05
1.42E-05
1.46E-06
7.64E-05
3.80E-06
4.46E-07
7.24E-06
7.09E-06
5.02E-05
6.45E-06
3.43E-05
1.41E+01
99%
UX
13.0644
5.33E-02
7.51E-02
0.0302895
0.86471
6.29E-03
7.92E-06
1.55E-06
3.03E-05
1.17E-04
6.26E-05
6.93E-07
1.23E-05
1.53E-05
3.00E-04
3.16E-06
1.32E-06
4.11E-06
6.36E-06
6.34E-05
7.46E-05
1.93E-05
1.73E-05
8.22E-06
1.81E-05
1.63E-07
8.46E-06
2.07E-05
2.47E-06
1.64E-05
2.33E-05
5.96E-06
2.08E-05
1.41E-05
2.73E-07
6.24E-05
8.41E-05
1.06E-06
2.08E-05
3.02E-10
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.344
2
3.395
3
3.629
4
7.513
5
7.784
6
8.989
7
11.335
8
13.667
9
14.693
10
15.021
11
17.523
12
18.295
13
19.039
14
19.586
15
19.992
16
21.107
17
22.263
18
23.317
19
24.024
20
24.646
21
24.926
22
26.032
23
26.592
24
26.844
25
27.259
26
27.298
27
29.243
28
29.600
29
29.853
30
30.097
31
31.241
32
31.485
33
31.846
34
32.079
35
33.134
36
33.770
37
34.367
38
34.737
39
36.213
40
36.646
SUM
Sum / Total mass
B-41
Damping 4%:
Mesh Size 1100mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.397
3.420
3.666
7.734
8.125
9.246
11.817
14.496
14.951
15.336
18.024
18.942
19.591
20.255
20.819
21.744
23.237
24.191
25.017
25.467
26.122
27.041
27.772
28.161
28.392
28.799
30.621
30.776
31.330
31.539
32.817
32.875
33.206
33.559
34.377
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
35.388
35.937
36.464
37.953
38.501
38.946
39.375
39.828
41.158
41.458
42.614
43.131
43.792
44.394
44.877
45.193
46.044
46.198
46.461
46.860
47.989
48.515
48.966
49.929
49.950
50.248
50.646
50.716
51.011
51.315
51.445
51.747
52.581
53.236
54.046
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-42
Freq
(Hz)
54.905
54.948
55.912
56.330
56.726
57.281
58.212
58.830
59.406
59.675
60.490
60.853
60.942
61.352
61.895
62.231
62.673
62.996
63.359
64.106
64.249
64.820
64.998
65.041
65.192
65.693
66.155
66.818
67.147
67.688
67.947
68.319
68.463
68.817
69.527
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
69.745
70.029
70.671
70.853
71.636
72.254
72.537
73.108
73.243
73.379
73.715
73.942
74.325
74.438
74.646
74.929
75.177
75.424
75.793
75.981
76.270
76.508
76.669
76.960
77.292
77.484
77.773
78.269
79.169
79.382
79.729
79.831
79.972
80.222
80.483
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.27E-04
1.80E-04
2.12E-06
1.78E-03
4.87E-03
3.34E-03
2.60E-03
8.91E-02
1.25E+01
1.23E-01
3.25E-03
8.25E-04
4.48E-04
4.73E-02
7.21E-02
5.14E-03
5.24E-03
1.64E-02
4.89E-04
1.75E-01
2.75E-01
1.68E-01
1.29E-02
8.36E-03
1.83E-03
2.49E-02
7.04E-03
9.48E-02
7.07E-02
3.48E-02
3.89E-02
6.81E-03
4.60E-02
9.91E-03
5.60E-02
6.87E-05
2.22E-04
1.06E-02
3.44E-02
1.44E-04
1.40E+01
98%
UY
0.169179
13.1976
5.43E-02
0.466307
1.74E-02
0.189501
3.08E-07
4.60E-05
7.01E-06
2.66E-07
3.64E-08
3.72E-05
2.58E-05
1.24E-07
6.46E-07
3.72E-05
8.82E-05
4.41E-07
1.18E-05
2.58E-05
2.13E-05
3.92E-06
3.65E-05
9.12E-06
6.39E-06
8.09E-05
1.96E-04
6.45E-07
2.87E-05
8.52E-05
6.72E-07
7.77E-06
2.95E-05
4.21E-05
4.08E-06
1.49E-06
9.26E-06
3.31E-05
1.33E-05
1.19E-05
1.41E+01
99%
UX
13.1022
1.53E-01
1.10E-01
0.009336
0.713133
5.99E-03
5.28E-06
2.04E-06
2.51E-05
6.50E-05
5.37E-05
2.98E-06
5.42E-06
3.02E-05
2.37E-04
5.16E-06
1.30E-06
3.60E-06
2.91E-05
4.63E-05
3.16E-05
4.13E-05
1.41E-05
1.14E-06
3.50E-07
3.35E-06
5.68E-06
5.57E-06
3.17E-06
5.30E-06
7.99E-09
3.08E-05
3.00E-06
1.08E-05
2.72E-07
1.36E-05
1.14E-04
1.58E-06
2.16E-05
4.81E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.397
2
3.420
3
3.666
4
7.734
5
8.125
6
9.246
7
11.817
8
14.496
9
14.951
10
15.336
11
18.024
12
18.942
13
19.591
14
20.255
15
20.819
16
21.744
17
23.237
18
24.191
19
25.017
20
25.467
21
26.122
22
27.041
23
27.772
24
28.161
25
28.392
26
28.799
27
30.621
28
30.776
29
31.330
30
31.539
31
32.817
32
32.875
33
33.206
34
33.559
35
34.377
36
35.388
37
35.937
38
36.464
39
37.953
40
38.501
SUM
Sum / Total mass
B-43
Damping 4%:
Mesh Size 500mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.733
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-44
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.265
58.431
59.028
59.185
59.557
59.714
60.251
60.744
61.274
61.460
62.329
62.813
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.626
65.592
66.000
66.166
66.601
66.988
67.168
67.513
67.949
68.570
68.744
68.941
69.150
69.421
69.452
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.665
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UY
UZ
UX
2.23E-04 0.0256597
12.4382
1.73E-02
2.56E-04
11.8483
1.67E-02
1.91E-06 1.05E+00
0.111228
3.28E-04
0.653839
1.5018
4.12E-03
8.07E-02
7.91E-03
2.63E-03
0.432494
2.57E-05
2.39E-03
4.17E-04
2.06E-06
2.50E-03
4.04E-04
9.60E-05
1.25E+01
9.93E-07
3.18E-04
8.35E-02
3.58E-06
1.21E-04
2.32E-07
8.99E-08
1.55E-08
3.48E-04
6.99E-07
1.30E-04
2.24E-01
1.20E-05
1.93E-04
3.78E-03
4.67E-06
7.15E-06
3.92E-03
9.21E-05
2.92E-05
1.52E-03
7.29E-05
2.44E-04
2.10E-02
1.99E-06
3.01E-06
7.15E-03
2.31E-04
2.09E-05
3.03E-02
2.80E-06
1.22E-05
2.12E-02
3.38E-06
3.79E-06
3.41E-03
4.71E-05
2.78E-04
3.27E-01
9.06E-06
9.58E-05
2.53E-01
7.11E-06
2.74E-05
4.40E-03
1.86E-04
7.97E-06
1.65E-03
9.01E-05
1.06E-05
1.23E-05
2.61E-05
1.44E-05
1.69E-02
2.81E-08
5.21E-06
1.51E-02
6.20E-04
1.30E-05
1.06E-02
4.23E-06
1.38E-04
3.85E-02
1.14E-04
2.29E-05
1.54E-01
9.77E-08
1.45E-05
7.93E-03
4.20E-06
1.46E-06
2.75E-04
4.50E-05
1.60E-06
7.10E-02
5.90E-05
8.59E-05
3.71E-02
4.42E-07
3.75E-05
7.91E-02
2.72E-07
2.14E-05
3.61E-03
3.16E-05
1.39E-05
4.55E-03
3.91E-06
5.93E-06
3.17E-03
3.67E-05
1.91E-05
4.02E-04
2.52E-05
1.39E+01
1.41E+01
1.41E+01
98%
99%
99%
Freq (Hz)
Mode No.
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-45
Damping 4%:
Mesh Size 800mm – 10-Nodded Element
MODAL FREQUENCY
Mode No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq (Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.276
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq (Hz)
30.753
31.529
32.381
32.646
33.117
33.922
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.171
40.131
40.891
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.070
45.535
46.030
46.194
47.486
47.801
48.405
Mode No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-46
Freq (Hz)
48.840
48.898
49.532
50.309
50.513
51.182
51.806
52.019
52.589
52.722
53.246
53.540
53.993
54.606
55.167
55.538
56.275
56.385
56.460
56.779
57.087
57.675
57.888
58.653
58.815
59.480
59.641
60.045
60.288
60.766
61.266
61.898
61.991
62.928
63.385
Mode No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq (Hz)
63.533
63.826
64.394
64.904
65.244
66.001
66.506
66.755
67.113
67.476
67.692
68.123
68.442
69.204
69.375
69.741
70.110
70.218
70.423
70.519
70.902
71.168
71.403
71.467
71.709
72.216
72.436
72.580
73.044
73.446
73.971
74.215
74.440
74.629
75.092
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
UY
UX
2.23E-04 0.0222106
12.4882
2.14E-04
11.7886
1.33E-02
2.14E-06 1.17E+00
1.94E-02
2.27E-04
0.631684
0.10322
3.92E-03
7.32E-02
1.46233
2.21E-03
0.405502
6.79E-03
2.14E-03
3.48E-04
2.44E-05
1.75E-03
3.93E-04
1.50E-06
1.22E+01
2.21E-07
3.68E-05
1.39E-01
3.87E-06
3.46E-04
5.42E-04
7.98E-07
3.85E-07
4.37E-04
1.55E-07
7.11E-05
2.59E-01
1.57E-05
5.25E-05
6.92E-04
1.80E-05
2.19E-04
1.34E-02
7.52E-05
2.31E-05
1.56E-02
1.95E-05
2.50E-04
1.72E-02
5.18E-05
4.95E-05
9.49E-03
2.08E-04
1.44E-06
2.28E-02
3.28E-06
2.33E-05
3.26E-02
1.05E-06
8.21E-06
9.79E-04
3.21E-05
4.94E-07
3.11E-01
4.45E-06
2.95E-04
3.51E-01
4.78E-06
7.02E-05
4.14E-03
1.39E-04
2.09E-05
6.02E-04
1.25E-04
1.18E-06
4.02E-05
3.05E-05
1.22E-05
1.96E-02
5.03E-07
1.05E-05
4.94E-03
5.48E-04
3.43E-06
8.36E-04
3.52E-06
6.56E-05
6.73E-04
1.43E-04
1.11E-04
1.44E-01
5.71E-06
3.55E-06
1.01E-01
1.08E-05
4.03E-06
9.21E-06
4.71E-05
1.62E-06
9.07E-02
5.22E-05
5.52E-06
4.31E-02
1.99E-08
9.34E-05
9.46E-02
7.80E-07
2.11E-05
4.39E-03
3.07E-05
2.80E-05
1.10E-03
5.18E-07
2.12E-05
7.32E-03
6.26E-05
1.62E-06
3.61E-04
6.56E-07
1.14E-05
1.39E+01
1.41E+01
1.41E+01
98%
99%
99%
Freq (Hz)
Mode No.
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.276
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-47
Damping 4%:
Mesh Size 1100mm – 10-Nodded Element
MODAL FREQUENCY
Mode No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq (Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.529
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.699
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq (Hz)
30.990
31.739
32.539
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.795
38.670
38.749
39.384
39.462
40.399
41.111
41.212
42.170
42.533
43.088
43.694
44.126
44.246
44.472
45.125
45.346
45.783
46.279
46.464
47.802
48.106
48.718
Mode No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-48
Freq (Hz)
49.202
49.298
49.836
50.656
50.876
51.554
52.125
52.322
52.892
53.054
53.567
53.886
54.304
54.950
55.639
55.985
56.656
56.755
56.793
57.123
57.543
58.097
58.338
59.117
59.224
59.876
60.095
60.488
60.800
61.289
61.750
62.325
62.541
63.456
63.852
Mode No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq (Hz)
63.952
64.385
65.002
65.396
65.765
66.417
66.993
67.221
67.646
68.004
68.226
68.680
68.969
69.782
69.820
70.319
70.746
70.803
71.125
71.191
71.485
71.741
71.923
71.963
72.251
72.934
73.044
73.179
73.759
74.173
74.637
74.875
75.234
75.306
75.665
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.11E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393026
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.20E-05
8.91E-07
5.12E-04
6.29E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
UX
12.5305
1.06E-02
2.17E-02
0.101603
1.42252
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
Freq (Hz)
Mode No.
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.529
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.699
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.539
39
32.862
40
33.441
SUM
Sum / Total mass
B-49
Damping 4%:
Mesh Size 500mm – 20-Nodded Element
MODAL FREQUENCY
Mode No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq (Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq (Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.734
45.898
47.070
47.419
48.036
Mode No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-50
Freq (Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.266
58.431
59.028
59.185
59.557
59.715
60.251
60.744
61.274
61.460
62.329
62.814
Mode No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq (Hz)
63.088
63.268
63.814
64.387
64.627
65.592
66.000
66.166
66.601
66.988
67.169
67.513
67.949
68.571
68.744
68.941
69.150
69.421
69.453
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.666
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.76E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
12.4382
1.73E-02
1.67E-02
0.111228
1.5018
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Freq (Hz)
Mode No.
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-51
Damping 4%:
Mesh Size 800mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.277
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.923
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.172
40.131
40.892
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.071
45.535
46.030
46.195
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-52
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.183
51.806
52.020
52.589
52.722
53.246
53.540
53.993
54.606
55.168
55.538
56.275
56.385
56.460
56.779
57.088
57.676
57.889
58.653
58.815
59.481
59.641
60.045
60.289
60.767
61.267
61.899
61.992
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.827
64.394
64.904
65.244
66.002
66.506
66.756
67.114
67.477
67.693
68.124
68.443
69.205
69.376
69.742
70.111
70.219
70.424
70.519
70.902
71.169
71.404
71.468
71.710
72.217
72.436
72.581
73.044
73.447
73.971
74.216
74.441
74.630
75.093
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.01E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.22E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405501
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.06E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.70E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.17E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
12.4882
1.33E-02
1.94E-02
0.10322
1.46233
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.26E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.277
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-53
Damping 4%:
Mesh Size 1100mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.530
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.700
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.540
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.796
38.671
38.749
39.385
39.462
40.399
41.112
41.212
42.170
42.534
43.089
43.694
44.127
44.247
44.473
45.125
45.346
45.784
46.280
46.465
47.803
48.106
48.719
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-54
Freq
(Hz)
49.202
49.298
49.837
50.657
50.877
51.555
52.126
52.323
52.893
53.055
53.568
53.887
54.305
54.951
55.640
55.986
56.657
56.756
56.793
57.124
57.544
58.098
58.339
59.118
59.226
59.877
60.096
60.489
60.802
61.291
61.752
62.327
62.543
63.457
63.853
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.953
64.386
65.004
65.397
65.767
66.419
66.995
67.222
67.648
68.006
68.228
68.682
68.972
69.785
69.822
70.320
70.748
70.805
71.126
71.192
71.487
71.743
71.925
71.965
72.253
72.936
73.046
73.181
73.761
74.175
74.639
74.878
75.236
75.309
75.667
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.12E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393025
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.21E-05
8.92E-07
5.12E-04
6.18E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
12.5305
1.06E-02
2.17E-02
0.101603
1.42252
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.530
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.700
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.540
39
32.862
40
33.441
SUM
Sum / Total mass
B-55
Damping 5%:
Mesh Size 500mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.263
3.348
3.560
7.114
7.355
8.627
10.740
12.604
14.335
14.567
16.915
17.328
18.587
18.777
19.115
20.339
21.179
22.252
22.916
23.471
23.693
23.972
25.038
25.809
25.903
26.318
27.981
28.458
28.621
28.884
29.288
30.068
30.181
30.763
31.420
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
31.962
32.937
33.364
34.442
34.932
35.386
35.744
36.055
37.461
37.872
38.973
39.204
40.076
40.218
40.946
41.431
42.454
42.940
43.194
43.529
43.791
44.858
44.906
46.111
46.272
46.286
46.638
46.871
47.187
47.593
48.424
48.902
49.429
49.953
51.018
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-56
Freq
(Hz)
51.401
52.245
52.360
52.498
52.911
53.459
53.766
53.958
54.542
55.325
55.816
56.241
56.481
56.964
57.185
57.517
57.955
58.444
58.732
59.122
59.752
60.182
60.675
61.290
61.983
62.339
62.857
63.132
63.687
63.949
64.245
64.803
65.135
65.318
66.145
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
66.837
66.875
67.726
67.975
68.493
68.960
69.294
69.428
70.000
70.523
70.779
70.833
70.978
71.315
71.575
71.728
72.149
72.237
72.322
72.479
73.167
73.354
73.553
73.932
73.995
74.349
74.520
74.989
75.416
75.487
75.871
75.984
76.272
76.580
76.777
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.58E-04
2.36E-04
7.35E-10
5.99E-04
4.35E-03
3.56E-03
2.33E-03
4.22E-03
1.19E+01
4.89E-01
1.96E-03
1.10E-03
1.06E-01
4.95E-02
7.57E-02
5.19E-03
4.87E-03
3.12E-03
2.96E-02
1.57E-02
5.49E-02
3.97E-01
2.31E-01
8.19E-03
1.68E-03
5.97E-03
8.36E-03
1.82E-02
1.85E-04
1.97E-01
4.29E-03
1.22E-02
4.12E-02
4.46E-02
4.13E-02
8.45E-02
7.54E-03
2.92E-04
1.01E-02
1.36E-04
1.39E+01
98%
UY
0.0238171
12.8363
3.36E-01
0.525275
6.17E-02
0.310454
7.05E-05
1.72E-04
5.66E-06
1.31E-07
2.60E-07
9.97E-07
4.02E-05
3.23E-05
3.98E-06
4.53E-05
1.75E-04
1.69E-06
3.28E-06
5.85E-06
2.46E-05
1.08E-05
1.83E-09
1.59E-04
5.36E-05
1.90E-06
4.56E-04
4.47E-05
4.26E-05
1.67E-05
1.79E-06
3.15E-05
1.88E-10
5.77E-05
7.17E-07
4.22E-07
4.84E-05
3.10E-06
2.03E-05
6.78E-06
1.41E+01
99%
UX
12.8409
1.57E-02
4.35E-02
0.0771418
1.11036
6.27E-03
1.50E-05
1.88E-06
1.71E-05
2.21E-04
5.88E-05
6.80E-08
2.49E-05
2.57E-05
3.34E-04
1.95E-06
8.47E-07
7.86E-07
4.96E-07
9.83E-07
3.77E-05
1.56E-04
7.98E-05
2.22E-07
3.08E-05
5.83E-06
9.95E-06
7.94E-05
4.74E-07
1.50E-05
1.12E-05
1.34E-05
7.16E-06
1.01E-06
8.00E-05
1.18E-05
6.96E-05
2.69E-05
5.04E-06
1.47E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.263
2
3.348
3
3.560
4
7.114
5
7.355
6
8.627
7
10.740
8
12.604
9
14.335
10
14.567
11
16.915
12
17.328
13
18.587
14
18.777
15
19.115
16
20.339
17
21.179
18
22.252
19
22.916
20
23.471
21
23.693
22
23.972
23
25.038
24
25.809
25
25.903
26
26.318
27
27.981
28
28.458
29
28.621
30
28.884
31
29.288
32
30.068
33
30.181
34
30.763
35
31.420
36
31.962
37
32.937
38
33.364
39
34.442
40
34.932
SUM
Sum / Total mass
B-57
Damping 5%:
Mesh Size 800mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.344
3.395
3.629
7.513
7.784
8.989
11.335
13.667
14.693
15.021
17.523
18.295
19.039
19.586
19.992
21.107
22.263
23.317
24.024
24.646
24.926
26.032
26.592
26.844
27.259
27.298
29.243
29.600
29.853
30.097
31.241
31.485
31.846
32.079
33.134
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
33.770
34.367
34.737
36.213
36.646
37.314
37.422
37.803
39.049
39.376
40.630
40.870
41.379
41.981
42.744
42.952
44.098
44.316
44.696
45.093
45.862
46.008
46.862
47.436
47.571
48.134
48.657
48.775
49.200
49.271
49.605
49.932
50.347
51.753
51.930
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-58
Freq
(Hz)
52.394
52.816
53.646
54.479
54.876
55.149
55.960
56.208
56.889
57.464
57.792
57.880
58.646
58.948
59.216
59.283
59.737
60.737
61.026
61.354
61.922
62.341
62.523
62.894
63.013
64.036
64.234
64.794
65.079
65.303
65.440
65.704
66.210
66.709
67.164
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
67.512
68.206
68.382
68.697
69.055
69.541
70.304
70.892
70.968
71.525
71.972
72.403
72.642
73.014
73.119
73.526
73.719
73.941
74.137
74.396
74.453
74.648
74.949
75.104
75.303
76.005
76.413
76.761
76.904
77.248
77.500
77.879
78.290
78.527
78.617
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.37E-04
2.04E-04
7.61E-07
1.15E-03
4.80E-03
3.51E-03
2.33E-03
1.43E-02
1.25E+01
8.17E-02
2.79E-03
7.22E-04
4.76E-03
7.61E-02
7.63E-02
4.03E-03
5.33E-03
1.37E-02
4.47E-02
1.02E-01
2.38E-01
2.63E-01
9.41E-03
2.07E-02
8.19E-03
3.01E-05
7.38E-03
8.69E-02
4.93E-04
1.30E-01
6.24E-02
9.51E-05
1.03E-02
4.87E-02
7.88E-02
5.35E-04
1.39E-04
8.21E-03
1.84E-02
8.50E-03
1.39E+01
98%
UY
0.0633402
13.183
9.89E-02
0.485796
3.50E-02
0.227832
1.27E-06
6.94E-05
5.62E-06
1.67E-07
1.55E-07
1.25E-05
5.62E-05
8.50E-07
9.40E-07
3.19E-05
1.41E-04
7.73E-07
1.40E-05
1.98E-05
2.49E-05
6.39E-06
2.53E-05
2.41E-05
8.31E-05
3.09E-05
3.55E-04
1.73E-05
2.23E-05
1.79E-05
1.42E-05
1.46E-06
7.64E-05
3.80E-06
4.46E-07
7.24E-06
7.09E-06
5.02E-05
6.45E-06
3.43E-05
1.41E+01
99%
UX
13.0644
5.33E-02
7.51E-02
0.0302895
0.86471
6.29E-03
7.92E-06
1.55E-06
3.03E-05
1.17E-04
6.26E-05
6.93E-07
1.23E-05
1.53E-05
3.00E-04
3.16E-06
1.32E-06
4.11E-06
6.36E-06
6.34E-05
7.46E-05
1.93E-05
1.73E-05
8.22E-06
1.81E-05
1.63E-07
8.46E-06
2.07E-05
2.47E-06
1.64E-05
2.33E-05
5.96E-06
2.08E-05
1.41E-05
2.73E-07
6.24E-05
8.41E-05
1.06E-06
2.08E-05
3.02E-10
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.344
2
3.395
3
3.629
4
7.513
5
7.784
6
8.989
7
11.335
8
13.667
9
14.693
10
15.021
11
17.523
12
18.295
13
19.039
14
19.586
15
19.992
16
21.107
17
22.263
18
23.317
19
24.024
20
24.646
21
24.926
22
26.032
23
26.592
24
26.844
25
27.259
26
27.298
27
29.243
28
29.600
29
29.853
30
30.097
31
31.241
32
31.485
33
31.846
34
32.079
35
33.134
36
33.770
37
34.367
38
34.737
39
36.213
40
36.646
SUM
Sum / Total mass
B-59
Damping 5%:
Mesh Size 1100mm – 8-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.397
3.420
3.666
7.734
8.125
9.246
11.817
14.496
14.951
15.336
18.024
18.942
19.591
20.255
20.819
21.744
23.237
24.191
25.017
25.467
26.122
27.041
27.772
28.161
28.392
28.799
30.621
30.776
31.330
31.539
32.817
32.875
33.206
33.559
34.377
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
35.388
35.937
36.464
37.953
38.501
38.946
39.375
39.828
41.158
41.458
42.614
43.131
43.792
44.394
44.877
45.193
46.044
46.198
46.461
46.860
47.989
48.515
48.966
49.929
49.950
50.248
50.646
50.716
51.011
51.315
51.445
51.747
52.581
53.236
54.046
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-60
Freq
(Hz)
54.905
54.948
55.912
56.330
56.726
57.281
58.212
58.830
59.406
59.675
60.490
60.853
60.942
61.352
61.895
62.231
62.673
62.996
63.359
64.106
64.249
64.820
64.998
65.041
65.192
65.693
66.155
66.818
67.147
67.688
67.947
68.319
68.463
68.817
69.527
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
69.745
70.029
70.671
70.853
71.636
72.254
72.537
73.108
73.243
73.379
73.715
73.942
74.325
74.438
74.646
74.929
75.177
75.424
75.793
75.981
76.270
76.508
76.669
76.960
77.292
77.484
77.773
78.269
79.169
79.382
79.729
79.831
79.972
80.222
80.483
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
1.27E-04
1.80E-04
2.12E-06
1.78E-03
4.87E-03
3.34E-03
2.60E-03
8.91E-02
1.25E+01
1.23E-01
3.25E-03
8.25E-04
4.48E-04
4.73E-02
7.21E-02
5.14E-03
5.24E-03
1.64E-02
4.89E-04
1.75E-01
2.75E-01
1.68E-01
1.29E-02
8.36E-03
1.83E-03
2.49E-02
7.04E-03
9.48E-02
7.07E-02
3.48E-02
3.89E-02
6.81E-03
4.60E-02
9.91E-03
5.60E-02
6.87E-05
2.22E-04
1.06E-02
3.44E-02
1.44E-04
1.40E+01
98%
UY
0.169179
13.1976
5.43E-02
0.466307
1.74E-02
0.189501
3.08E-07
4.60E-05
7.01E-06
2.66E-07
3.64E-08
3.72E-05
2.58E-05
1.24E-07
6.46E-07
3.72E-05
8.82E-05
4.41E-07
1.18E-05
2.58E-05
2.13E-05
3.92E-06
3.65E-05
9.12E-06
6.39E-06
8.09E-05
1.96E-04
6.45E-07
2.87E-05
8.52E-05
6.72E-07
7.77E-06
2.95E-05
4.21E-05
4.08E-06
1.49E-06
9.26E-06
3.31E-05
1.33E-05
1.19E-05
1.41E+01
99%
UX
13.1022
1.53E-01
1.10E-01
0.009336
0.713133
5.99E-03
5.28E-06
2.04E-06
2.51E-05
6.50E-05
5.37E-05
2.98E-06
5.42E-06
3.02E-05
2.37E-04
5.16E-06
1.30E-06
3.60E-06
2.91E-05
4.63E-05
3.16E-05
4.13E-05
1.41E-05
1.14E-06
3.50E-07
3.35E-06
5.68E-06
5.57E-06
3.17E-06
5.30E-06
7.99E-09
3.08E-05
3.00E-06
1.08E-05
2.72E-07
1.36E-05
1.14E-04
1.58E-06
2.16E-05
4.81E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.397
2
3.420
3
3.666
4
7.734
5
8.125
6
9.246
7
11.817
8
14.496
9
14.951
10
15.336
11
18.024
12
18.942
13
19.591
14
20.255
15
20.819
16
21.744
17
23.237
18
24.191
19
25.017
20
25.467
21
26.122
22
27.041
23
27.772
24
28.161
25
28.392
26
28.799
27
30.621
28
30.776
29
31.330
30
31.539
31
32.817
32
32.875
33
33.206
34
33.559
35
34.377
36
35.388
37
35.937
38
36.464
39
37.953
40
38.501
SUM
Sum / Total mass
B-61
Damping 5%:
Mesh Size 500mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.733
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-62
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.265
58.431
59.028
59.185
59.557
59.714
60.251
60.744
61.274
61.460
62.329
62.813
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.626
65.592
66.000
66.166
66.601
66.988
67.168
67.513
67.949
68.570
68.744
68.941
69.150
69.421
69.452
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.665
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.77E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
12.4382
1.73E-02
1.67E-02
0.111228
1.5018
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-63
Damping 5%:
Mesh Size 800mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.276
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.922
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.171
40.131
40.891
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.070
45.535
46.030
46.194
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-64
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.182
51.806
52.019
52.589
52.722
53.246
53.540
53.993
54.606
55.167
55.538
56.275
56.385
56.460
56.779
57.087
57.675
57.888
58.653
58.815
59.480
59.641
60.045
60.288
60.766
61.266
61.898
61.991
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.826
64.394
64.904
65.244
66.001
66.506
66.755
67.113
67.476
67.692
68.123
68.442
69.204
69.375
69.741
70.110
70.218
70.423
70.519
70.902
71.168
71.403
71.467
71.709
72.216
72.436
72.580
73.044
73.446
73.971
74.215
74.440
74.629
75.092
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.02E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.21E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405502
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.05E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.71E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.18E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
12.4882
1.33E-02
1.94E-02
0.10322
1.46233
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.25E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.276
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-65
Damping 5%:
Mesh Size 1100mm – 10-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.529
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.699
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.539
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.795
38.670
38.749
39.384
39.462
40.399
41.111
41.212
42.170
42.533
43.088
43.694
44.126
44.246
44.472
45.125
45.346
45.783
46.279
46.464
47.802
48.106
48.718
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-66
Freq
(Hz)
49.202
49.298
49.836
50.656
50.876
51.554
52.125
52.322
52.892
53.054
53.567
53.886
54.304
54.950
55.639
55.985
56.656
56.755
56.793
57.123
57.543
58.097
58.338
59.117
59.224
59.876
60.095
60.488
60.800
61.289
61.750
62.325
62.541
63.456
63.852
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.952
64.385
65.002
65.396
65.765
66.417
66.993
67.221
67.646
68.004
68.226
68.680
68.969
69.782
69.820
70.319
70.746
70.803
71.125
71.191
71.485
71.741
71.923
71.963
72.251
72.934
73.044
73.179
73.759
74.173
74.637
74.875
75.234
75.306
75.665
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.11E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393026
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.20E-05
8.91E-07
5.12E-04
6.29E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
12.5305
1.06E-02
2.17E-02
0.101603
1.42252
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.529
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.699
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.539
39
32.862
40
33.441
SUM
Sum / Total mass
B-67
Damping 5%:
Mesh Size 500mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.143
3.256
3.453
6.636
6.899
8.141
9.971
11.364
13.502
13.713
15.843
16.053
17.552
18.078
18.357
18.859
19.103
19.640
21.343
21.730
22.263
22.577
23.445
23.895
24.331
24.561
25.341
26.194
26.912
26.989
27.105
27.500
28.552
29.207
30.021
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.449
31.261
32.150
32.336
32.535
33.629
33.701
34.159
34.936
35.883
36.207
36.806
37.136
38.063
38.184
38.675
38.870
39.731
40.589
40.706
41.667
41.872
42.411
43.190
43.571
43.747
43.903
44.585
44.739
45.250
45.734
45.898
47.070
47.419
48.036
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-68
Freq
(Hz)
48.380
48.556
49.211
49.959
50.151
50.768
51.441
51.696
52.262
52.371
52.931
53.190
53.667
54.248
54.622
55.168
55.824
56.024
56.099
56.437
56.702
57.266
57.493
58.266
58.431
59.028
59.185
59.557
59.715
60.251
60.744
61.274
61.460
62.329
62.814
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.088
63.268
63.814
64.387
64.627
65.592
66.000
66.166
66.601
66.988
67.169
67.513
67.949
68.571
68.744
68.941
69.150
69.421
69.453
69.695
69.943
70.589
70.885
70.952
71.059
71.210
71.644
72.043
72.247
72.597
73.237
73.532
73.666
73.988
74.055
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.56E-04
1.91E-06
3.28E-04
4.12E-03
2.63E-03
2.39E-03
2.50E-03
1.25E+01
8.35E-02
2.32E-07
3.48E-04
2.24E-01
3.78E-03
3.92E-03
1.52E-03
2.10E-02
7.15E-03
3.03E-02
2.12E-02
3.41E-03
3.27E-01
2.53E-01
4.40E-03
1.65E-03
1.23E-05
1.69E-02
1.51E-02
1.06E-02
3.85E-02
1.54E-01
7.93E-03
2.75E-04
7.10E-02
3.71E-02
7.91E-02
3.61E-03
4.55E-03
3.17E-03
4.02E-04
1.39E+01
98%
UY
0.0256597
11.8483
1.05E+00
0.653839
8.07E-02
0.432494
4.17E-04
4.04E-04
9.93E-07
3.58E-06
8.99E-08
6.99E-07
1.20E-05
4.67E-06
9.21E-05
7.29E-05
1.99E-06
2.31E-04
2.80E-06
3.38E-06
4.71E-05
9.06E-06
7.11E-06
1.86E-04
9.01E-05
2.61E-05
2.81E-08
6.20E-04
4.23E-06
1.14E-04
9.76E-08
4.20E-06
4.50E-05
5.90E-05
4.42E-07
2.72E-07
3.16E-05
3.91E-06
3.67E-05
2.52E-05
1.41E+01
99%
UX
12.4382
1.73E-02
1.67E-02
0.111228
1.5018
7.91E-03
2.57E-05
2.06E-06
9.60E-05
3.18E-04
1.21E-04
1.55E-08
1.30E-04
1.93E-04
7.15E-06
2.92E-05
2.44E-04
3.01E-06
2.09E-05
1.22E-05
3.79E-06
2.78E-04
9.58E-05
2.74E-05
7.97E-06
1.06E-05
1.44E-05
5.21E-06
1.30E-05
1.38E-04
2.29E-05
1.45E-05
1.46E-06
1.60E-06
8.59E-05
3.75E-05
2.14E-05
1.39E-05
5.93E-06
1.91E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.143
2
3.256
3
3.453
4
6.636
5
6.899
6
8.141
7
9.971
8
11.364
9
13.502
10
13.713
11
15.843
12
16.053
13
17.552
14
18.078
15
18.357
16
18.859
17
19.103
18
19.640
19
21.343
20
21.730
21
22.263
22
22.577
23
23.445
24
23.895
25
24.331
26
24.561
27
25.341
28
26.194
29
26.912
30
26.989
31
27.105
32
27.500
33
28.552
34
29.207
35
30.021
36
30.449
37
31.261
38
32.150
39
32.336
40
32.535
SUM
Sum / Total mass
B-69
Damping 5%:
Mesh Size 800mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.164
3.279
3.477
6.685
6.955
8.281
10.059
11.452
13.930
14.120
16.170
16.292
17.821
18.201
18.442
19.277
19.545
20.079
21.449
22.002
22.595
23.053
23.627
24.178
24.752
24.885
25.481
26.489
27.142
27.254
27.729
27.868
28.767
29.428
30.238
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.753
31.529
32.381
32.646
33.117
33.923
34.029
34.564
35.227
36.182
36.560
37.263
37.506
38.390
38.487
39.071
39.172
40.131
40.892
40.945
41.933
42.227
42.810
43.451
43.891
44.004
44.211
44.872
45.071
45.535
46.030
46.195
47.486
47.801
48.405
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-70
Freq
(Hz)
48.840
48.898
49.532
50.309
50.513
51.183
51.806
52.020
52.589
52.722
53.246
53.540
53.993
54.606
55.168
55.538
56.275
56.385
56.460
56.779
57.088
57.676
57.889
58.653
58.815
59.481
59.641
60.045
60.289
60.767
61.267
61.899
61.992
62.928
63.385
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.533
63.827
64.394
64.904
65.244
66.002
66.506
66.756
67.114
67.477
67.693
68.124
68.443
69.205
69.376
69.742
70.111
70.219
70.424
70.519
70.902
71.169
71.404
71.468
71.710
72.217
72.436
72.581
73.044
73.447
73.971
74.216
74.441
74.630
75.093
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.23E-04
2.14E-04
2.14E-06
2.27E-04
3.92E-03
2.21E-03
2.14E-03
1.75E-03
1.22E+01
1.39E-01
5.42E-04
4.37E-04
2.59E-01
6.92E-04
1.34E-02
1.56E-02
1.72E-02
9.49E-03
2.28E-02
3.26E-02
9.79E-04
3.11E-01
3.51E-01
4.14E-03
6.02E-04
4.01E-05
1.96E-02
4.94E-03
8.36E-04
6.73E-04
1.44E-01
1.01E-01
9.22E-06
9.07E-02
4.31E-02
9.46E-02
4.39E-03
1.10E-03
7.32E-03
3.61E-04
1.39E+01
98%
UY
0.0222106
11.7886
1.17E+00
0.631684
7.32E-02
0.405501
3.48E-04
3.93E-04
2.21E-07
3.87E-06
7.98E-07
1.55E-07
1.57E-05
1.80E-05
7.52E-05
1.95E-05
5.18E-05
2.08E-04
3.28E-06
1.05E-06
3.21E-05
4.45E-06
4.78E-06
1.39E-04
1.25E-04
3.06E-05
5.03E-07
5.48E-04
3.52E-06
1.43E-04
5.70E-06
1.08E-05
4.71E-05
5.22E-05
1.99E-08
7.80E-07
3.07E-05
5.17E-07
6.26E-05
6.56E-07
1.41E+01
99%
UX
12.4882
1.33E-02
1.94E-02
0.10322
1.46233
6.79E-03
2.44E-05
1.50E-06
3.68E-05
3.46E-04
3.85E-07
7.11E-05
5.26E-05
2.19E-04
2.31E-05
2.50E-04
4.95E-05
1.44E-06
2.33E-05
8.21E-06
4.94E-07
2.95E-04
7.02E-05
2.09E-05
1.18E-06
1.22E-05
1.05E-05
3.43E-06
6.56E-05
1.11E-04
3.55E-06
4.03E-06
1.62E-06
5.52E-06
9.34E-05
2.11E-05
2.80E-05
2.12E-05
1.62E-06
1.14E-05
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.164
2
3.279
3
3.477
4
6.685
5
6.955
6
8.281
7
10.059
8
11.452
9
13.930
10
14.120
11
16.170
12
16.292
13
17.821
14
18.201
15
18.442
16
19.277
17
19.545
18
20.079
19
21.449
20
22.002
21
22.595
22
23.053
23
23.627
24
24.178
25
24.752
26
24.885
27
25.481
28
26.489
29
27.142
30
27.254
31
27.729
32
27.868
33
28.767
34
29.428
35
30.238
36
30.753
37
31.529
38
32.381
39
32.646
40
33.117
SUM
Sum / Total mass
B-71
Damping 5%:
Mesh Size 1100mm – 20-Nodded Element
MODAL FREQUENCY
Mode
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Freq
(Hz)
3.178
3.294
3.490
6.729
6.999
8.347
10.129
11.536
14.161
14.323
16.274
16.530
17.957
18.291
18.522
19.525
19.809
20.290
21.538
22.198
22.790
23.256
23.805
24.385
25.006
25.118
25.584
26.700
27.333
27.458
28.016
28.157
28.980
29.597
30.416
Mode
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
Freq
(Hz)
30.990
31.739
32.540
32.862
33.441
34.133
34.260
34.840
35.509
36.433
36.862
37.597
37.796
38.671
38.749
39.385
39.462
40.399
41.112
41.212
42.170
42.534
43.089
43.694
44.127
44.247
44.473
45.125
45.346
45.784
46.280
46.465
47.803
48.106
48.719
Mode
No.
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
B-72
Freq
(Hz)
49.202
49.298
49.837
50.657
50.877
51.555
52.126
52.323
52.893
53.055
53.568
53.887
54.305
54.951
55.640
55.986
56.657
56.756
56.793
57.124
57.544
58.098
58.339
59.118
59.226
59.877
60.096
60.489
60.802
61.291
61.752
62.327
62.543
63.457
63.853
Mode
No.
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Freq
(Hz)
63.953
64.386
65.004
65.397
65.767
66.419
66.995
67.222
67.648
68.006
68.228
68.682
68.972
69.785
69.822
70.320
70.748
70.805
71.126
71.192
71.487
71.743
71.925
71.965
72.253
72.936
73.046
73.181
73.761
74.175
74.639
74.878
75.236
75.309
75.667
EFFECTIVE MASS OF THE FIRST 40 MODES
UZ
2.02E-04
2.03E-04
6.24E-07
2.46E-04
3.67E-03
1.85E-03
2.11E-03
1.70E-03
1.17E+01
4.91E-01
5.40E-04
9.25E-03
2.58E-01
5.08E-03
2.94E-02
1.69E-02
2.03E-02
9.93E-03
1.91E-02
3.69E-02
1.06E-03
3.01E-01
4.03E-01
3.66E-03
1.06E-03
1.40E-04
1.85E-02
3.44E-03
2.51E-04
2.09E-04
7.19E-02
1.83E-01
1.12E-05
9.72E-02
4.65E-02
1.04E-01
4.20E-03
1.13E-03
9.44E-03
8.01E-04
1.38E+01
98%
UY
0.0193855
11.8724
1.13E+00
0.609558
7.09E-02
0.393025
3.90E-04
4.02E-04
9.40E-08
5.37E-06
4.45E-07
7.55E-08
1.60E-05
3.29E-05
5.30E-05
1.91E-05
5.12E-05
1.96E-04
3.32E-06
5.74E-07
2.74E-05
3.79E-06
4.08E-06
1.37E-04
1.11E-04
4.21E-05
8.92E-07
5.12E-04
6.18E-09
1.59E-04
1.62E-05
3.67E-06
4.56E-05
4.71E-05
1.66E-07
1.10E-06
2.98E-05
1.68E-06
6.17E-05
3.11E-08
1.41E+01
99%
UX
12.5305
1.06E-02
2.17E-02
0.101603
1.42252
6.36E-03
2.28E-05
1.31E-06
1.64E-05
3.33E-04
1.77E-07
6.46E-05
2.41E-05
2.13E-04
5.64E-05
2.28E-04
5.21E-05
8.95E-07
2.71E-05
8.00E-06
6.45E-07
2.89E-04
5.65E-05
1.87E-05
1.15E-06
1.06E-05
8.45E-06
3.71E-06
9.51E-05
7.81E-05
5.96E-06
9.80E-07
1.28E-06
8.07E-06
9.40E-05
1.67E-05
3.22E-05
2.09E-05
2.63E-06
8.48E-06
1.41E+01
99%
Mode
No.
Freq (Hz)
1
3.178
2
3.294
3
3.490
4
6.729
5
6.999
6
8.347
7
10.129
8
11.536
9
14.161
10
14.323
11
16.274
12
16.530
13
17.957
14
18.291
15
18.522
16
19.525
17
19.809
18
20.290
19
21.538
20
22.198
21
22.790
22
23.256
23
23.805
24
24.385
25
25.006
26
25.118
27
25.584
28
26.700
29
27.333
30
27.458
31
28.016
32
28.157
33
28.980
34
29.597
35
30.416
36
30.990
37
31.739
38
32.540
39
32.862
40
33.441
SUM
Sum / Total mass
B-73
APPENDIX (C)
SEISMIC CALCULATION
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
C-11
C-12
C-13