Table of Contents
ANSYS Mechanical
Dynamics
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Table of Contents
Training Manual
1. Introduction to Dynamics
Definition & Purpose
Types of Dynamic Analysis
Basic Concepts and Terminology
Damping
Workshop 1 – Flywheel
1-1
1-6
1-9
1-15
1-21
1-33
5. Random Vibration Analysis
Definition & Purpose
Power Spectral Density
Workbench capabilities
Procedure
Workshop 5 – Girder Assembly
5-1
5-3
5-5
5-9
5-10
5-22
2. Modal Analysis
Definition & Purpose
Terminology & Concepts
Procedure
Workshop 2A – Plate with Hole
Workshop 2B – Prestressed Wing
2-1
2-3
2-5
2-21
2-40
2-40
3. Harmonic Response Analysis
Definition & Purpose
Terminology & Concepts
Procedure
Workshop 5 – Fixed-Fixed Beam
3-1
3-3
3-5
3-17
3-31
6. Transient Analysis
Introduction
Preliminary Modal Analysis
Including Nonlinearities
Part Specification and Meshing
Nonlinear Materials
Contact; Joints; and Springs
Initial Conditions
Loads; Supports; Joint Conditions
Damping
Analysis Settings
Reviewing Results
Workshop 6 – Caster
6-1
6-4
6-7
6-10
6-17
6-19
6-20
6-27
6-30
6-32
6-33
6-35
6-37
4. Response Spectrum Analysis
Definition & Purpose
Response Calculations
Mode Combination
Procedure
Workshop 4 – Suspension Bridge
4-1
4-3
4-8
4-12
4-14
4-25
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Chapter 1:
Introduction
ANSYS Mechanical
Dynamics
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Introduction
Welcome!
Training Manual
• Welcome to the Workbench Dynamics training course!
• This training course covers the procedures required to perform
dynamic analyses with ANSYS Workbench.
• It is intended for novice and experienced users.
• A related course is ANSYS Rigid and Flexible Dynamic Analysis,
which covers multi-body analysis.
• Several other advanced training courses are available on specific
topics.
– See the training course schedule on the ANSYS homepage:
www.ansys.com under “Training Services”.
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Introduction
Course Objectives
Training Manual
• This course is intended for users already familiar with the procedures
for performing a linear static analysis in Workbench Mechanical
environment.
– Prerequisite is ANSYS Workbench – Mechanical Introduction
• By the end of this course, you will be able to use Mechanical to
define, solve, and interpret the following dynamic analyses:
–
–
–
–
–
Modal
Harmonic Response
Response Spectrum
Random Vibration
Transient
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Introduction
Course Material
Training Manual
• The Training Manual you have is an exact copy of the slides.
• Workshop descriptions and instructions are included in the
Workshop Supplement.
• Copies of the workshop files are available (upon request) from the
instructor.
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Introduction
Introduction to Dynamics
Training Manual
A. Define dynamic analysis and its purpose.
B. Discuss different types of dynamic analysis available in Workbench
Mechanical.
C. Cover some basic concepts and terminology.
D. Review the types of damping available in Workbench Mechanical.
E. Do a sample dynamic analysis exercise.
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Dynamics
A. Definition & Purpose
Training Manual
• A dynamic analysis is a technique used to determine the dynamic
behavior of a structure or component.
• It is an analysis involving time, where the inertia and possibly
damping of the structure play an important role.
• “Dynamic behavior” may be one or more of the following:
– Vibration characteristics
• how the structure vibrates and at what frequencies
–
–
–
–
Effect of harmonic loads.
Effect of seismic or shock loads.
Effect of random loads.
Effect of time-varying loads.
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Dynamics
… Definition & Purpose
Training Manual
• A static analysis might ensure
that the design will withstand
steady-state loading conditions,
but it may not be sufficient,
especially if the load varies with
time.
• The famous Tacoma Narrows
bridge (Galloping Gertie)
collapsed under steady wind
loads during a 42-mph wind
storm on November 7, 1940, just
four months after construction.
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Dynamics
… Definition & Purpose
Training Manual
• A dynamic analysis usually takes into account one or more of the
following:
– free vibrations
• natural vibration frequencies and shapes
– forced vibrations
• e.g. crank shafts, other rotating machinery
– seismic/shock loads
• e.g. earthquake, blast
– random vibrations
• e.g. rocket launch, road transport
– time-varying loads
• e.g. car crash, hammer blow
• Each situation is handled by a specific type of dynamic analysis.
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Dynamics
B. Types of Dynamic Analysis
Training Manual
• Consider the following examples:
– An automobile tailpipe assembly could shake apart if its natural frequency
matched that of the engine. How can you avoid this?
– A turbine blade under stress (centrifugal forces) shows different dynamic behavior.
How can you account for it?
• A modal analysis can be used to determine a structure’s vibration
characteristics.
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Dynamics
… Types of Dynamic Analysis
Training Manual
– Rotating machines exert steady,
alternating forces on bearings and
support structures. These forces
cause different deflections and
stresses depending on the speed of
rotation.
• A harmonic-response analysis can
be used to determine a structure’s
response to steady, harmonic loads.
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Dynamics
… Types of Dynamic Analysis
Training Manual
– Spacecraft and aircraft components must withstand random loading of varying
frequencies for a sustained time period.
A random-vibration analysis can be used to determine how a component
responds to random vibrations.
Courtesy: NASA
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Dynamics
… Types of Dynamic Analysis
Training Manual
– Skyscrapers, power-plant cooling
towers, and other structures must
withstand multiple short-duration
transient shock/impact loadings,
common in seismic events.
• A response-spectrum analysis can
be used to determine how a
component responds to
earthquakes.
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Dynamics
… Types of Dynamic Analysis
Training Manual
– An automobile fender should be able to withstand low-speed impact, but deform
under higher-speed impact.
– A tennis racket frame should be designed to resist the impact of a tennis ball and
yet flex somewhat.
• A transient analysis can be used to calculate a structure’s response to time
varying loads.
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Dynamics
… Types of Dynamic Analysis
Training Manual
• Choosing the appropriate type of dynamic analysis depends on the type of
input available and the type of output desired.
Type
Input
Output
Modal
• none
• natural frequencies and
corresponding mode shapes
• stress/strain profile
Harmonic
• sinusoidally-varying excitations
across a range of frequencies
• sinusoidally-varying response at
each frequency
• min/max response over frequency
range
Spectrum
• spectrum representing the
response to a specific time history
• maximum response if the model
were subjected to the time history
Random
• spectrum representing probability
distribution of excitation
• response within specified range of
probabilities
Transient
• time-varying loads
• time-varying response
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Dynamics
C. Basic Concepts and Terminology
Training Manual
Topics discussed:
• General equation of motion
• Modeling considerations
• Damping
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Basic Concepts & Terminology
Equation of Motion
Training Manual
• The linear general equation of motion, which will be referred to
throughout this course, is as follows (matrix form):
M u C u K u F
u nodal accelerati on vector
M structural mass matrix
C structural damping matrix u nodal velocity vector
K structural stiffness matrix u nodal displaceme nt vector
F applied load vector
• Note that this is simply a force balance:
Finertial
Fdamping
Fstiffness
applied
F
M u C u K u F
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Basic Concepts & Terminology
Equation of Motion
Training Manual
M u C u K u F
• Different analysis types solve different forms of this equation.
– Modal
• F(t) set to zero; [C] usually ignored.
– Harmonic Response
• F(t) and u(t) assumed to be sinusoidal.
– Response Spectrum
• Input is a known spectrum of response magnitudes at varying frequencies in
known directions.
– Random Vibration
• Input is a probabilistic spectrum of input magnitudes at varying frequencies in
known directions.
– Transient
• The complete, general form of the equation is solved.
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Basic Concepts & Terminology
Modeling Considerations - Geometry and Mesh
Training Manual
• Generally same geometry and meshing considerations for static
analysis apply to dynamic analysis.
– Include as many details as necessary to sufficiently represent the model
mass distribution.
– A fine mesh will be needed in areas where stress results are of interest. If
you are only interested in displacement results, a coarse mesh may be
sufficient.
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Basic Concepts & Terminology
Modeling Considerations - Nonlinearities
Training Manual
M u C u
K u u F
nonlinear
• Nonlinearities, such as large deflections, nonlinear contact, material
nonlinearities, etc, are allowed only in a full transient dynamic
analysis with large deflection turned ON.
• All other Workbench dynamic analysis types are linear.
– the initial state of nonlinearities will be maintained throughout the
solution; i.e., [K] = const.
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Basic Concepts & Terminology
Modeling Considerations - Material properties
Training Manual
M u Cu K u F
• Mass properties [M]
–
–
–
–
e.g. density, point mass
required for all dynamic analysis types
specify mass density when using metric units, and
specify weight density when using British units
• Damping properties [C]
– e.g. viscous, material (discussed later)
– required for mode-superposition harmonic
– optional but recommended for all other dynamic analysis types
• Stiffness (elastic) properties [K]
– e.g., Young’s modulus, Poisson’s ratio, shear modulus
– required for all flexible analysis types
• Note that Mechanical has display (interactive) units and solution units.
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Basic Concepts & Terminology
D. Damping
Training Manual
• Damping is an energy-dissipation
mechanism that causes vibrations
to diminish over time and eventually
stop.
– e.g. vibrational energy that is
converted to heat or sound
• The amount of damping may
depend on the material, the velocity
of motion, and/or the frequency of
vibration.
• Damping be classified as:
– Viscous damping (e.g. dashpot,
shock absorber)
– Material / Solid / Hysteretic damping
(e.g. internal friction)
– Coulomb or dry-friction damping
(e.g. sliding friction)
– Numerical damping
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Basic Concepts & Terminology
Damping
Training Manual
• If the amount of damping in a system
becomes large, the response will no
longer oscillate.
• Critical damping is defined as the
threshold between oscillatory and
non-oscillatory behavior.
• The damping ratio is the ratio of the
damping in a system to the critical
damping, given by
c
cc
cc 2m
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k
2 km 2mn
m
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Basic Concepts & Terminology
Damping
Training Manual
• The undamped natural frequency of a
1-DOF system is given by
n
k
m
d
1 2
n
• The addition of viscous or solid
damping slightly alters the natural
frequency of a system.
d 1 2 n
• Coulomb damping has no effect on
frequency.
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Basic Concepts & Terminology
Viscous damping
Training Manual
• Viscous damping force is
proportional to the velocity of the
vibrating body.
Fd cu
• Assuming the motion is harmonic,
Fd cu icnu
• This type of damping occurs, for
example, when a body moves
through a fluid.
c k
Fd ku i k n u
• For structural systems, a stiffness
multiplier is often used in place of c
for numerical simplicity.
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Basic Concepts & Terminology
Viscous damping
Training Manual
• The value of c in
Fd cu icnu
can be input directly as element damping
(Details section of Spring connection).
• The value of in
Fd ku iknu
can be input directly as global
damping value (Details section of
Analysis Settings) or as materialdependent damping value
(Material Damping Factor material
property).
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Basic Concepts & Terminology
Material / Solid / Hysteretic damping
Training Manual
• Solid damping is inherently present
in a material (energy is dissipated
by internal friction), so it is typically
considered in a dynamic analysis.
• Experience shows that energy
dissipated by internal friction in a
real system does not depend on
frequency.
• Not well understood and therefore
difficult to quantify, so again a
stiffness multiplier is used for
numerical simplicity.
Fd 2iku
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Basic Concepts & Terminology
Material / Solid / Hysteretic damping
Training Manual
• The value of in
Fd 2iku
can be input directly as global
damping value (Details section
of Analysis Settings) or as
material-dependent damping
value (Constant Damping
Coefficient material property).
• Damping ratio isn’t available in a transient analysis since
the response frequency is not known in advance.
– The value of can be calculated from a known value of
(damping ratio) and a known frequency :
2 / n
– Pick the most dominant response frequency to calculate .
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Basic Concepts & Terminology
Coulomb or dry-friction damping
Training Manual
• Coulomb damping occurs when a body slides on a dry surface.
• Damping force is proportional to the force normal to the surface.
Fd mmg sgn(x )
–
–
–
–
m is the coefficient of friction
m is the mass
g is the gravitational constant
sgn(y) is the signum function, defined as
1 for y 0
sgn( y ) 1 for y 0
0 for y 0
• Not considered in a linear dynamic analysis. Generally requires a
nonlinear transient solution.
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Basic Concepts & Terminology
Numerical Damping
Training Manual
• Numerical Damping is not true damping.
– Artificially controls numerical noise produced by the higher frequencies of a
structure.
• Stabilizes the numerical integration scheme by damping out the unwanted
high frequency modes.
• The default value of 10% will damp-out spurious high frequencies and is a
sensible value to try initially.
• Use the lowest possible value that damps out nonphysical response without
significantly affecting the final solution.
High-frequency
response
Primary
Frequency
undamped
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Basic Concepts & Terminology
Damping – Summary
Training Manual
• In summary, Workbench allows the
following four inputs for damping:
– Beta damping (viscous)
• Global or material-dependent.
• Defines the stiffness matrix multiplier
for damping.
– Element damping (viscous)
• Defines the damping coefficients
directly.
– Damping ratio (solid)
• Global or material-dependent.
• Defines the ratio of actual damping to
critical damping.
– Numerical damping (artificial)
• Defines the amplitude decay factor
obtained through a modification of
the time-integration scheme.
• NOTE: The effects are cumulative if
set in conjunction.
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Basic Concepts & Terminology
Damping
Training Manual
• Different industries specify damping in different ways:
h
Q
D
D
A
= Viscous damping factor or damping ratio
= Loss factor or Structural damping factor
= Quality factor or simply
= Log decrement
= Spectral damping factor
= Amplification factor
• The following table provides the conversions (note: U = strain energy)
Measure
Spectral
Damping
Amplification
Factor
1/(2Q)
D/(4pU)
1/2A
D/p
1/Q
D/(2pU)
1/A
ph
D
p/Q
D/(2U)
p/A
1/2
1/h
p/D
Q
2pU/D
A
4pU
2pUh
2UD
2pU/Q
D
2pU/A
1/2
1/h
p/D
Q
2pU/D
A
Damping ratio
Loss Factor
Damping Ratio
h/2
D/2p
Loss Factor
2
h
Log Decrement
2p
Quality Factor
Spectral
Damping
Amplification
Factor
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Log Decrement Quality Factor
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Dynamics
References & Bibliography
Training Manual
• S. S. Rao, Mechanical Vibrations.
• K. Ogata, Modern Control Engineering.
• B. J. Lazan, Damping of Materials and Members in Structural
Mechanics.
• A. K. Gupta, Response Spectrum Method: In Seismic Analysis and
Design of Structures.
• U.S. Nuclear Regulatory Commission Regulatory Guide 1.92,
Combining Modal Responses and Spatial Components in Seismic
Response Analysis.
• D. E. Newland, An Introduction to Random Vibrations, Spectral &
Wavelet Analysis.
• Military Standard 810E, Environmental Test Methods And
Engineering Guidelines.
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Dynamics
E. Introductory Workshop
Training Manual
• In this workshop, you will run a
sample dynamic analysis of a
flywheel.
• Follow the instructions in your
Dynamics Workshop supplement
WS1: Intro (Flywheel)
• The idea is to introduce you to the
steps involved in a typical dynamic
analysis. Details of what each step
means will be covered in the rest of
this seminar.
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Chapter 2:
Modal Analysis
ANSYS Mechanical
Dynamics
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Modal Analysis
Training Manual
A. Define modal analysis and its purpose.
B. Discuss associated concepts, terminology, and mode extraction
methods.
C. Learn how to do a modal analysis in Workbench.
D. Work on one or two modal analysis exercises.
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Description & Purpose
Training Manual
• A modal analysis is a technique used to determine the vibration
characteristics of structures:
– natural frequencies
• at what frequencies the structure would tend to naturally vibrate
– mode shapes
• in what shape the structure would tend to vibrate at each frequency
– mode participation factors
• the amount of mass that participates in a given direction for each mode
• Most fundamental of all the dynamic analysis types.
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Description & Purpose
Training Manual
Benefits of modal analysis
• Allows the design to avoid resonant vibrations or to vibrate at a
specified frequency (speaker box, for example).
• Gives engineers an idea of how the design will respond to different
types of dynamic loads.
• Helps in calculating solution controls (time steps, etc.) for other
dynamic analyses.
Recommendation: Because a structure’s vibration characteristics
determine how it responds to any type of dynamic load, it is generally
recommended to perform a modal analysis first before trying any other
dynamic analysis.
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Description & Purpose
Terminology
Training Manual
• A “mode” refers to the pair of one
natural frequency and
corresponding mode shape.
mode 1
← {f}1
f1 = 109 Hz
– A structure can have any number of
modes, up to the number of DOF in
the model.
mode 2
← {f}2
f2 = 202 Hz
mode 3
← {f}3
f3 = 249 Hz
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Theory
Assumptions & Restrictions
Training Manual
• The structure is linear (i.e. constant stiffness and mass).
• There is no damping.
– Damped eigensolvers (MODOPT,DAMP or MODOPT,QRDAMP) may be
accessed using Commands Objects, but will not be covered here.
• The structure has no time varying forces, displacements, pressures,
or temperatures applied (free vibration).
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Theory
Development
Training Manual
• Start with the linear general equation of motion:
M u C u K u F
• Assume free vibrations, and ignore damping:
0
0
M u C u K u F
M u K u 0
• Assume harmonic motion:
u
u
u
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f i
i f i
i2 f i
sin i t i
cosi t i
sin i t i
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Theory
Development
Training Manual
• Substitute and simplify
M u K u 0
i2 M f i sin i t i K f i sin i t i 0
i2 M K fi 0
• This equality is satisfied if fi = 0 (trivial, implies no vibration) or if
det K i2 M 0
• This is an eigenvalue problem which may be solved for up to n
eigenvalues, i2, and n eigenvectors, fi, where n is the number of
DOF.
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Theory
Extraction & Normalization
Training Manual
• Note that the equation
det K M 0
2
i
has one more unknown than equations; therefore, an additional
equation is needed to find a solution.
– The addition equation is provided by mode shape normalization.
• Mode shapes can be normalized either to the mass matrix
f M fi 1
T
i
or to unity, where the largest component of the vector {f}i is set to 1.
• Workbench displays results normalized to the mass matrix.
• Because of this normalization, only the shape of the DOF solution
has real meaning.
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Theory
Eigenvalues & Eigenvectors
Training Manual
• The square roots of the eigenvalues
are i, the structure’s natural
circular frequencies (rad/s).
mode 1
← {f}1
f1 = 109 Hz
• Natural frequencies fi can then
calculated as fi = i/2p (cycles/s).
– It is the natural frequencies, fi in Hz,
that are input by the user and output
by Workbench.
mode 2
← {f}2
f2 = 202 Hz
• The eigenvectors {f}i represent the
mode shapes, i.e. the shape
assumed by the structure when
vibrating at frequency fi.
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mode 3
← {f}3
f3 = 249 Hz
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Theory
Equation Solvers
• The equation
Training Manual
det K M 0
2
i
can be solved using one of two solvers available in Workbench
Mechanical:
– Direct (Block Lanczos)
• To find many modes (about 40+) of large models.
• Performs well when the model consists of shells or a combination of shells
and solids.
• Uses the Lanczos algorithm where the Lanczos recursion is performed with a
block of vectors. Uses the sparse matrix solver.
– Iterative (PCG Lanczos)
• To find few modes (up to about 100) of very large models (500,000+ DOFs).
• Performs well when the lowest modes are sought for models that are
dominated by well-shaped 3-D solid elements.
• Uses the Lanczos algorithm, combined with the PCG iterative solver.
• In most cases, the Program Controlled option selects the optimal
solver automatically.
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Theory
Participation Factors (Solution Information)
Training Manual
• The participation factors are calculated by
i f Ti M D
where {D} is an assumed unit displacement spectrum in each of the global
Cartesian directions and rotation about each of these axes.
– This measures the amount of mass moving in each direction for each mode.
– The “Ratio” is simply another list of participation factors, normalized to the largest.
• The concept of participation factors will be important in later chapters.
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Theory
Participation Factors (Solution Information)
Training Manual
• A high value in a direction indicates that the mode will be excited by forces in
that direction.
mode 1
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Theory
Effective Mass (Solution Information)
Training Manual
• Also printed out is the effective mass.
M eff ,i
i2
f M f i
T
i
2
i
, if f M f i 1
T
i
• Ideally, the sum of the effective masses in each direction should equal total
mass of structure, but will depend on the number of modes extracted.
• The ratio of effective mass to total mass can be useful for determining
whether or not a sufficient number of modes have been extracted.
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Theory
Prestress Effects
Training Manual
• A prestressed modal analysis can be used to calculate the
frequencies and mode shapes of a prestressed structure, such as a
spinning turbine blade.
– The prestress influences the stiffness of the structure through the stressstiffening matrix contribution.
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Theory
Prestress Effects
Training Manual
• In free vibration with prestress analyses, two solutions are required.
– A linear static analysis is initially performed:
K u F s
– Based on the stress state [s] from the static analysis, a stress stiffness
matrix [S] is calculated (see Theory Reference for details):
s S
– The free vibration with pre-stress analysis is then solved, including the [S]
term:
K S M f 0
2
i
i
• Note that the prestress only affects the stiffness of the system.
– i.e. the static prestress will not be added to the modal stress
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Remarks & Comments
Contact Regions
Training Manual
• Contact regions are available in modal analysis; however, since this
is a purely linear analysis, contact behavior will differ for the
nonlinear contact types, as shown below:
Linear Dynamic Analysis
Contact Type
Static Analysis
Initially Touching
Inside Pinball Region
Outside Pinball
Region
Bonded
Bonded
Bonded
Bonded
Free
No Separation
No Separation
No Separation
No Separation
Free
Rough
Rough
Bonded
Free
Free
Frictionless
Frictionless
No Separation
Free
Free
Frictional
Frictional
m = 0, No Separation
m > 0, Bonded
Free
Free
• Contact behavior will reduce to its linear counterparts.
– It is generally recommended, however, not to use a nonlinear contact
type in a linear-dynamic analysis
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Remarks & Comments
Unconstrained Systems
Training Manual
• An unconstrained system is one that has no constraints or supports
and can move as a rigid body in at least one direction.
– Rigid-body motion can be considered to be a mode of oscillation with
zero frequency.
– In practice, these modes may not have a frequency of exactly zero.
“rigid-body”
or
“zero” modes
• Note that a well-connected system can have at most six rigid-body
modes.
– Obtaining more than six rigid-body modes may indicate that assemblies
are not well connected.
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Remarks & Comments
Symmetry Boundary Conditions
Training Manual
• Symmetry BC’s will only produce symmetrically shaped modes, so
some modes can be missed.
– It may be necessary to apply several different symmetry conditions to
find all modes.
– The full model below results in the frequencies listed in the tabular view.
– A quarter-symmetry model will require three sets of symmetry boundary
conditions to find all modes (see next slide)...
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Remarks & Comments
Symmetry Boundary Conditions
Training Manual
Symm-Asym BC
Full Model
Symmetry BC
etc
Anti-Symmetry BC
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Procedure:
Modal
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Modal
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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Modal
Procedure
Training Manual
• Create new geometry, or link to
existing geometry.
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• Edit the Model cell to bring up the
Mechanical application.
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Modal
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings.
– This was covered in Workbench Mechanical Intro.
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Modal
Preprocessing
Training Manual
• Add supports to the model.
– Displacement constrains must have a magnitude of zero.
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Modal
Solution Settings
Training Manual
• Choose the number of modes to
extract.
• If needed, upper and lower bounds
on frequency may be specified to
extract the modes within a specified
range.
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Modal
Solution Settings
Training Manual
• Stress and strain results may be
turned on under Output Controls.
• If the Program-Controlled solver
selection is not appropriate, the
solver type can be changed to
either Direct or Iterative.
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Modal
Postprocessing
Training Manual
• Total-deformation results may be
quickly inserted by highlighting
multiple rows in the tabular view or
histogram view.
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Modal
Postprocessing
Training Manual
• If stress/strain were requested, these results may also be access from the
Solution Toolbar.
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Procedure:
Prestressed Modal
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Prestressed Modal
Procedure
Training Manual
• The procedure to do a prestressed
modal analysis is essentially the
same as a regular modal analysis,
except that you first need to
prestress the structure by doing a
static analysis.
• The static analysis results in a
stressed structure, which is used as
the initial condition for the modal
analysis.
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Prestressed Modal
Procedure
Training Manual
• Drop a Static Structural (ANSYS) system into the project schematic.
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Prestressed Modal
Procedure
Training Manual
• Drop a Modal (ANSYS) system onto
the Solution cell of the Modal
system.
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• Note the circular-ended connector,
indicating a data transfer from the
Static to the Modal analysis.
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Prestressed Modal
Procedure
Training Manual
• Create new geometry, or link to
existing geometry.
• Edit the Model cell to bring up the
Mechanical application.
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Prestressed Modal
Preprocessing
Training Manual
• In the Static Structural system, insert the loads and supports that will cause
the prestressed-state to occur.
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Prestressed Modal
Postprocessing
Training Manual
• Review the static results before
proceeding.
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Prestressed Modal
Preprocessing
Training Manual
• Workbench will automatically setup
the data transfer between the
systems.
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• To verify the data transfer, one can
ensure that
– Future Analysis is set to
Prestressed analysis in the Static
Structural system
– Pre-Stress Environment is set to
Static Structural in the Modal
system
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Prestressed Modal
Postprocessing
Training Manual
• The modal results may be reviewed as described in the previous section.
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Prestressed Modal
Postprocessing
Training Manual
• Note that the prestressed state increased the frequencies of this structure.
– e.g. the first mode in this example increased from 108.3 Hz to 274.6 Hz
Not Prestressed
Prestressed
• A prestress may not always increase the natural frequencies; a compressive
load will decrease the frequencies.
– In fact, a sufficiently-high compressive load will result in a natural frequency of
zero, effectively replicating the results of a buckling analysis.
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D. Workshop - Modal Analysis
Training Manual
This workshop consists of two problems:
1. Modal analysis of a plate with a hole
– A step-by-step description of how to do the analysis.
– You may choose to run this problem yourself, or your instructor may
show it as a demonstration.
(WS2A: Modal Analysis - Plate with a Hole).
2. Pre-stressed Modal analysis of a model airplane wing
– This is left as an exercise to you.
(WS2B: Modal Analysis - Model Airplane Wing).
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Chapter 3:
Harmonic Response
ANSYS Mechanical
Dynamics
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Harmonic Analysis
Harmonic Analysis
Training Manual
A. Define harmonic analysis and its purpose.
B. Learn basic terminology and concepts underlying harmonic
analysis.
C. Learn how to do a harmonic analysis in Workbench.
D. Work on a harmonic analysis exercise.
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Harmonic Analysis
A. Definition & Purpose
Training Manual
What is harmonic analysis?
• A technique to determine the steady state response of a structure to
sinusoidal (harmonic) loads of known frequency.
• Input:
– Harmonic loads (forces, pressures, and imposed displacements) of
known magnitude and frequency.
– May be multiple loads all at the same frequency. Forces and
displacements can be in-phase or out-of phase. Body loads can only be
specified with a phase angle of zero.
• Output:
– Harmonic displacements at each DOF, usually out of phase with the
applied loads.
– Other derived quantities, such as stresses and strains.
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Harmonic Analysis
… Definition & Purpose
Training Manual
Harmonic analysis is used in the design of:
• Supports, fixtures, and components of rotating equipment such as
compressors, engines, pumps, and turbomachinery.
• Structures subjected to vortex shedding (swirling motion of fluids)
such as turbine blades, airplane wings, bridges, and towers.
Why should you do a harmonic analysis?
• To make sure that a given design can withstand sinusoidal loads at
different frequencies (e.g, an engine running at different speeds).
• To detect resonant response and avoid it if necessary (by using
dampers, for example).
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Harmonic Analysis
B. Terminology & Concepts
Training Manual
Topics covered:
• Assumptions and Restrictions
• Equation of motion
• Nature of harmonic loads
• Complex displacements
• Solution methods
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Theory
Assumptions & Restrictions
Training Manual
• The entire structure has constant or frequency-dependent stiffness,
damping, and mass effects.
• All loads and displacements vary sinusoidally at the same known
frequency (although not necessarily in phase).
• Acceleration, bearing, and moment loads are assumed to be real (inphase) only.
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Theory
Development
Training Manual
• Start with the linear general equation of motion:
M u C u K u F
• Assume [F] and {u} are harmonic with frequency W:
F Fmax ei eiWt
u umax ei eiWt
Fmax cos i sin eiW t
umax cos i sin eiW t
F1 iF2 eiW t
u 1 iu2 eiW t
• Note: The symbols W an w differentiate the input from the output:
W = input (a.k.a. imposed) circular frequency
w = output (a.k.a. natural) circular frequency
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Theory
Development
Training Manual
• Take two time derivatives:
u
u
u
iW
W2
u 1 iu2 eiWt
u 1 iu2 eiWt
u 1 iu2 eiWt
• Substitute and simplify:
M u C u K u F
W 2 M u 1 iu2 eiW t
iWC u 1 iu2 eiW t
K u 1 iu2 eiW t F 1 iF2 eiW t
W 2 M iWC K u 1 iu2 F 1 iF2
• This can then be solved using one of two methods.
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Theory
Development
Training Manual
• The full method solves the system of simultaneous equations directly
using a static solver designed for complex arithmetic:
– c denotes a complex matrix or vector
Kc
uc
Fc
W2 M iWC K u 1 iu2 F 1 iF2
K c uc Fc
• The mode-superposition method expresses the displacements as a
linear combination of mode shapes (see Theory Reference for details).
W M iWC K u iu F iF
2
1
W
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2
2
1
2
i 2w j W j w 2j y jc f jc
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Theory
Solution Methods
Training Manual
FULL
MSUP
• Exact solution.
• Approximate solution; accuracy depends in
part on whether an adequate number of
modes have been extracted to represent
the harmonic response.
• Generally slower than MSUP.
• Generally faster than FULL.
• Supports all types of loads and boundary
conditions.
• Does not support nonzero imposed
harmonic displacements.
• Solution points must be equally distributed
across the frequency domain.
• Solution points may be either equally
distributed across the frequency domain or
clustered about the natural frequencies of
the structure.
• Solves the full system of simultaneous
• Solves an uncoupled system of equations
equations using the Sparse matrix solver for
by performing a linear combination of
complex arithmetic.
orthogonal vectors (mode shapes).
• Prestressing is not available in either method in ANSYS Workbench 12.0.
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Theory
Nature of Harmonic Loads
Training Manual
• Multiple loads and boundary
conditions may be input, each with
different amplitude and phase
angles (interpreted as lag angle).
xi X i sin wt i
where X amplitude
w freqency
phase angle
• All loads and displacements, both
input and output, are assumed to
occur at the same frequency.
• Calculated displacements will be
complex if
– damping is specified or
– applied load is complex.
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Remarks & Comments
Resonance
Training Manual
• When the imposed frequency
approaches a natural frequency in
the direction of excitation, a
phenomenon known as resonance
occurs.
– This can be seen in the figures on
the right for a 1-DOF system
subjected to a harmonic force for
various amounts of damping.
• The following will be observed:
– an increase in damping decreases
the amplitude of the response for all
imposed frequencies,
– a small change in damping has a
large effect on the response near
resonance, and
– the phase angle always passes
through ±90° at resonance for any
amount of damping.
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Remarks & Comments
Contact Regions
Training Manual
• Contact regions are available in harmonic analysis; however, since
this is a purely linear analysis, contact behavior will differ for the
nonlinear contact types, as shown below:
Linear Dynamic Analysis
Contact Type
Static Analysis
Initially Touching
Inside Pinball Region
Outside Pinball
Region
Bonded
Bonded
Bonded
Bonded
Free
No Separation
No Separation
No Separation
No Separation
Free
Rough
Rough
Bonded
Free
Free
Frictionless
Frictionless
No Separation
Free
Free
Frictional
Frictional
m = 0, No Separation
m > 0, Bonded
Free
Free
• Contact behavior will reduce to its linear counterparts.
– It is generally recommended, however, not to use a nonlinear contact
type in a linear-dynamic analysis
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Remarks & Comments
Mode Superposition
Training Manual
• The Mode Superposition method will automatically perform a modal
analysis first
– The number of modes necessary for an accurate solution will be
estimated if a frequency range is not supplied.
• the default range is from zero to twice the ending frequency
– The harmonic analysis portion is very quick and efficient, hence, the
Mode Superposition method is usually much faster overall than the Full
method
• Since a free vibration analysis is performed, Mechanical knows what
the natural frequencies of the structure are and can cluster the
harmonic results near them (see next slide)
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Remarks & Comments
… Solution Methods - Mode Superposition
Training Manual
• Cluster option captures the peak response better than evenly-spaced
intervals.
Evenly spaced
frequency points
Clustered frequency
points
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Procedure:
Harmonic Response
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Harmonic Analysis
C. Procedure
Training Manual
Four main steps:
• Build the model
• Choose analysis type and options
• Apply harmonic loads and solve
• Review results
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Harmonic Analysis Procedure
Build the Model
Training Manual
Model
• Nonlinearities are not allowed.
• See also Modeling Considerations in Module 1.
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Harmonic Analysis Procedure
Choose Analysis Type & Options
Training Manual
Build the model
Choose analysis type and options
• Enter Solution and choose
harmonic analysis.
• Main analysis option is solution
method - discussed next.
• Specify damping - discussed
next.
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Harmonic Analysis Procedure
… Choose Analysis Type & Options
Analysis options
• Solution method - full or mode
superposition.
• For large models (>1 million
DOF), set Store Results at All
Frequencies to “No”.
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Training Manual
Damping
• Choose from beta damping and
damping ratio (constant
damping ratio is most
commonly used).
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Harmonic Analysis Procedure
Apply Harmonic Loads and Solve
Training Manual
Build the model
Choose analysis type and options
Apply harmonic loads and solve
• Structural loads and supports may also be used in harmonic
analyses with the following exceptions:
– Loads Not Supported:
•
•
•
•
•
Gravity Loads
Thermal Loads
Rotational Velocity
Pretension Bolt Load
Compression Only Support (if present, it behaves similar to a Frictionless
Support)
• Remember that all structural loads will vary sinusoidally at the same
excitation frequency
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Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• A list of supported loads are shown below:
– Not all available loads support phase input. Accelerations, Bearing Load,
and Moment Load will have a phase angle of 0°.
• If other loads are present, shift the phase angle of other loads, such that the
Acceleration, Bearing, and Moment Loads will remain at a phase angle of 0°.
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Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Specifying harmonic loads requires:
– Amplitude and phase angle
– Frequency
• Amplitude and phase angle
– The load value (magnitude) represents
the amplitude Fmax.
– Phase angle Y is the phase shift
between two or more harmonic loads.
Not required if only one load is present.
Non-zero Y valid for force,
displacement, and pressure harmonic
loads.
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Imaginary
• Loads are applied all at once in the first
solution interval (stepped).
F2max
F1max
Real
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Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Amplitude and phase angle (continued)
Imaginary
– Mechanical allows direct input of amplitude and phase angle into the
Details window.
F2max
F1max
Real
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Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Frequency of harmonic load:
– Specified in cycles per second
(Hertz) by a frequency range and
number of substeps within that
range.
– For example, a range of 0-50 Hz
with 10 solution intervals gives
solutions at frequencies of 5, 10,
15, …, 45, and 50 Hz. Same
range with 1 substep gives one
solution at 50 Hz.
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Harmonic Analysis Procedure
Review Results
Training Manual
Build the model
Choose analysis type and options
Apply harmonic loads and solve
Review results
• Three steps:
– Plot displacement vs. frequency at specific points in the structure.
– Identify critical frequencies and corresponding phase angles.
– Review displacements and stresses over entire structure at the
critical frequencies and phase angles.
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Harmonic Analysis Procedure
Review Results
Training Manual
Displacement vs. frequency plots
• Pick nodes that might deform the
most, then choose the DOF
direction.
• Then graph the desired frequency
response.
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Harmonic Analysis Procedure
… Review Results
Training Manual
Identify critical frequencies and phase angles
• Bode plot shows frequency at which highest amplitude occurs.
• The amplitude and phase angle at which the peak amplitude occurs
are shown in the Worksheet tab.
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Harmonic Analysis Procedure
… Review Results
Training Manual
• Next step is to review displacements and stresses over the entire
model at that frequency and phase angle.
• The frequency and phase angle must be manually entered into the
Details window.
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Harmonic Analysis Procedure
… Review Results
Training Manual
• A harmonic analysis produces a real and imaginary solution as
separate sets of results.
• Plot deformed shape, stress contours, and other desired results at
a specified frequency and phase angle.
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Workshop
Harmonic Analysis
Training Manual
• In this workshop, you will examine the harmonic response of a
fixed-fixed beam to harmonic forces caused by rotating
machinery mounted on the beam.
• See your Dynamics Workshop supplement for details
WS3: Harmonic Analysis - Fixed-Fixed Beam
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Chapter 4:
Response Spectrum
ANSYS Mechanical
Dynamics
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Response Spectrum Analysis
Training Manual
Topics covered:
• Definition and purpose
• Overview of Workbench capabilities
• Procedure
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Response Spectrum Analysis
Description & Purpose
Training Manual
• A response-spectrum analysis
calculates the maximum response
of a structure to a transient loading.
• It is performed as a fast alternative
of approximating a full transient
solution.
• The maximum response is
computed as scale factor times the
mode shape.
• These maximum responses are then
combined to give a total response
of the structure.
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Response Spectrum Analysis
Types of Analyses
Training Manual
Types of Response Spectrum analysis:
• Single-point response spectrum
– A single response spectrum excites all specified points in the model.
• Multi-point response spectrum
– Different response spectra excite different points in the model.
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Response Spectrum Analysis
Common Uses
Training Manual
• Commonly used in the analysis of:
– Nuclear power plant buildings
and components, for seismic
loading
– Airborne Electronic equipment
for shock loading
– Commercial buildings in
earthquake zones
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Response Spectrum Analysis
Terminology & Concepts
Training Manual
• Instead of simulating the response of a structure to a full time history,
we could figure out how each mode would respond to the time
history, then combine the responses together.
• In other words, the response of each mode of a structure is similar to
a 1-DOF oscillator, just scaled by some amount.
• If we know the natural frequencies and mode shapes of a structure,
we can simply determine what the displacement would be for a 1-DOF
oscillator, if it were subjected to the same transient loading, and
scale the response by the appropriate amount.
• If there is more than one load, each will have its own spectrum.
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Response Spectrum Analysis
Assumptions & Restrictions
Training Manual
• The structure is linear (i.e. constant stiffness and mass).
• For single-point response spectrum analysis, the structure is excited
by a spectrum of known direction and frequency components, acting
uniformly on all support points.
• For multi-point response spectrum analysis, the structure may be
excited by different input spectra at different support points.
– Up to 20 different simultaneous input spectra are allowed.
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Theory
Participation Factors
Training Manual
• A modal analysis must first be completed to determine the natural
frequencies, mode shapes, and participation factors for each mode.
– This procedure was covered in Chapter 2: Modal Analysis.
M K 0
2
i
i
i M D
T
i
mode
frequency
mode shape
spectrum
value
participation
factor
mode
coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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Theory
Spectrum Values
Training Manual
• For each natural frequency, the spectrum value can be determined by a
simple look-up from the response-spectrum table.
– When values are needed between input frequencies, log-log interpolation is done
in the space as defined.
mode
frequency
mode shape
spectrum
value
participation
factor
mode
coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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Theory
Mode Coefficients
Training Manual
• The mode coefficients can be determined from the participation factors,
depending on the type of spectrum input.
displaceme nt
Ai Si i
velocity
S
Ai i i
i
accelerati on
S
Ai i 2i
i
– Recall: participation factors measure the amount of mass moving in each direction
for a unit displacement.
mode
frequency
mode shape
spectrum
value
participation
factor
mode
coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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Theory
Response
Training Manual
• The response (displacement, velocity or acceleration) for each mode can
then be computed from the frequency, mode coefficient, and mode shape.
Ri
Ri
Ri
Ai i
i Ai i
i2 Ai i
for displaceme nt response
for veloci ty response
for accelerati on response
• If there is more than one significant mode, the response for each mode must
be combined using some method.
mode
frequency
mode shape
spectrum
value
participation
factor
mode
coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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Theory
Mode Combination
Training Manual
• In general, mode combinations take the form:
N N
R e ij Ri Rj
i 1 j 1
1
2
where R is the total modal response and RiRj is the entrywise product
(a.k.a. Hadamard or Schur product) of modes i and j.
• The modal correlation coefficients, eij, are uniquely defined,
depending on the method chosen for evaluating the correlation
coefficient.
e ij 1
for partially correlated modes i and j 0 e ij 1
for uncorrelat ed correlated modes i and j
e ij 0
for completely correlated modes i and j
• The methods for mode combination are SRSS, CQC, and ROSE.
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Theory
Mode Combination
Training Manual
• The SRSS method is generally more conservative than the other
methods.
– assumes that all maximum modal values are uncorrelated
e ij 1.0 for i j
e ij 0.0 for i j
– for a structures with coupled modes, this assumption overestimates the
responses overall
• The CQC and the ROSE methods providing a means of evaluating
modal correlation for the response spectrum analysis.
– accounting for mode coupling makes the response estimate from these
methods more realistic and closer to the exact time history solution
SRSS
R Ri2
i 1
N
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CQC
1
2
R ke ij Ri Rj
i 1 j 1
N
N
4-13
ROSE
1
2
R e ij Ri Rj
i 1 j 1
N
N
1
2
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Procedure:
Response Spectrum
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Response Spectrum
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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Response Spectrum
Procedure
Training Manual
• Drop a Response Spectrum system onto the Solution cell of the
Modal system.
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Response Spectrum
Procedure
Training Manual
• Create new geometry, or link to
existing geometry.
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• Edit the Model cell to bring up the
Mechanical application.
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Response Spectrum
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings.
– This was covered in Workbench Mechanical Intro.
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Response Spectrum
Preprocessing
Training Manual
• Add supports to the model.
– Displacement constrains must have a magnitude of zero.
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Response Spectrum
Solution Settings
Training Manual
• Choose the number of modes to
extract.
• If needed, upper and lower bounds
on frequency may be specified to
extract the modes within a specified
range.
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Response Spectrum
Postprocessing
Training Manual
• Review the modal results before
proceeding.
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Response Spectrum
Preprocessing
Training Manual
• Insert an Acceleration, Velocity, or Direction response spectrum.
• Set the Boundary Condition, Spectrum (Tabular) Data, and Direction.
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Response Spectrum
Postprocessing
Training Manual
• Insert Directional Deformation, Velocity, or Acceleration.
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Response Spectrum
Postprocessing
Training Manual
• Stress (normal, shear, equivalent) and Strain (normal, shear) results
can also be reviewed.
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Workshop
Response Spectrum Analysis
Training Manual
• In this workshop, you will determine the response of a
prestressed suspension bridge subjected to a seismic load.
• See your Dynamics Workshop supplement for details
WS4: Response Spectrum Analysis - Suspension Bridge
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Chapter 5:
Random Vibration
ANSYS Mechanical
Dynamics
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Random Vibration Analysis
Random Vibration Analysis
Training Manual
Topics covered:
• Definition and purpose
• Overview of Workbench capabilities
• Procedure
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Random Vibration Analysis
A. Definition and Purpose
Training Manual
What is random vibration analysis?
– A spectrum analysis technique based on probability and statistics.
– Meant for loads such as acceleration loads in a rocket launch that
produce different time histories during every launch .
Reference: Random vibrations in mechanical systems by Crandall & Mark
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Random Vibration Analysis
… Definition
and Purpose
Training Manual
• Transient analysis is not an option since the time history is not
deterministic (sample is not repeatable).
• Instead, using statistics the sample time histories are converted to
Power Spectral Density function (PSD), a statistical representation of
the load time history.
Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.
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Random Vibration Analysis
Power Spectral Density
Training Manual
• Sample time histories are converted to Power Spectral Density
function (PSD), a statistical representation of the load time history.
Reference: Random vibrations in
mechanical systems by Crandall
& Mark
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Image from “Random Vibrations Theory and
Practice” by Wirsching, Paez and Ortiz.
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Random Vibration Analysis
Statistical Representation
Training Manual
• A Random Vibration analysis computes the probability distribution of
different results, such as displacement or stress, due to some
random excitation
• The analysis follows a modal analysis
• An internal combination is done to compute the combined effect from
each mode and their interactions.
Gaussian
(normal)
Distribution
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Random Vibration Analysis
Power Spectral Density
Training Manual
• The Power Spectral Density is the
mean square value of the excitation
for a unit frequency band.
– The area under a PSD curve is
the variance of the response
(square of the standard
deviation).
– The units used in PSD are mean
square/Hz (e.g. an acceleration
PSD will have units of G2/Hz).
– The quantity represented by
PSD may be displacement,
velocity, acceleration, force, or
pressure.
Random Vibration curve by MIL-STD-202
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Random Vibration Analysis
Common Uses
Training Manual
• Commonly used for
– Airborne electronics
– Acoustic loading of Airframe parts
– Jitter in alignment of optical
equipment
– Relative deformation in large
mirrors
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Random Vibration
Workbench Capabilities
Training Manual
• Input:
– Natural frequencies and mode shapes from a modal analysis
– Single or multiple PSD excitations applied to ground nodes
• Output:
– 1s results can be contoured like any other analysis.
– Response PSD at one DOF (one point in one direction)
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Procedure:
Random Vibration
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Random Vibration
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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Random Vibration
Procedure
Training Manual
• Drop a Random Vibration system onto the Solution cell of the Modal
system.
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Random Vibration
Procedure
Training Manual
• Create new geometry, or link to
existing geometry.
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• Edit the Model cell to bring up the
Mechanical application.
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Random Vibration
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings.
– This was covered in Workbench Mechanical Intro.
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Random Vibration
Preprocessing
Training Manual
• Add supports to the model.
– Displacement constrains must have a magnitude of zero.
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Random Vibration
Solution Settings
Training Manual
• Choose the number of modes to
extract.
• If needed, upper and lower bounds
on frequency may be specified to
extract the modes within a specified
range.
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Random Vibration
Postprocessing
Training Manual
• Review the modal results before
proceeding.
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Random Vibration
Preprocessing
Training Manual
• Insert an Acceleration, Velocity, or Direction PSD base excitation.
• Set the Boundary Condition, Load (Tabular) Data, and Direction.
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Random Vibration
Postprocessing
Training Manual
• Insert Directional Deformation, Velocity, or Acceleration.
– the direction and sigma value may be chosen here
– note that results are always reviewed with scaling set to 0.0
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Random Vibration
Postprocessing
Training Manual
• Stress (normal, shear, equivalent) and Strain (normal, shear) results
can also be reviewed.
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Random Vibration
Postprocessing
Training Manual
• Response PSD can be plotted at one DOF (one point in one direction,
either absolute or relative to base excitation).
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Workshop – Random Vibration
Training Manual
• In workshop 5A, you will determine the displacements and stresses
in a girder assembly due to an acceleration PSD.
WS5A: Random Vibration (PSD) Analysis of a Girder Assembly
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Chapter 6:
Transient
ANSYS Mechanical
Dynamics
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Overview
Training Manual
• Transient structural analysis provides users with the ability to
determine the dynamic response of the system under any type of
time-varying loads.
– Unlike rigid dynamic analyses, bodies can be either rigid or flexible. For
flexible bodies, nonlinear materials can be included, and stresses and
strains can be output.
– Transient structural analysis is also known as time-history analysis or
transient structural
analysis.
– To perform Flexible
Dynamic Analyses, an
ANSYS Structural,
ANSYS Mechanical, or
ANSYS Multiphysics
license is required
Assembly shown here is from an Autodesk Inventor sample model
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Topics Covered
Training Manual
Background Information:
A. Introduction to Transient Structural Analyses
B. Preliminary Linear Dynamic Studies
C. Background Information on Nonlinear Analyses
Procedural Information:
D. Demo – Impact Problem
E. Part Specification and Meshing
F. Nonlinear Materials
G. Contact; Joints; and Springs
H. Initial Conditions
I. Loads; Supports; and Joint Conditions
J. Damping
K. Transient Structural Analysis Settings
L. Reviewing Results
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A. Introduction
Training Manual
• Transient structural analyses are needed to evaluate the response of
deformable bodies when inertial effects become significant.
– If inertial and damping effects can be ignored, consider performing a
linear or nonlinear static analysis instead
– If the loading is purely sinusoidal and the response is linear, a harmonic
response analysis is more efficient
– If the bodies can be assumed to be rigid and the kinematics of the system
is of interest, rigid dynamic analysis is more cost-effective
– In all other cases, transient structural analyses should be used, as it is
the most general type of dynamic analysis
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… Introduction
Training Manual
• In a transient structural analysis, Workbench Mechanical solves the
general equation of motion:
M x C x K xx F t
Some points of interest:
– Applied loads and joint conditions may be a function of time and space.
– As seen above, inertial and damping effects are now included. Hence,
the user should include density and damping in the model.
– Nonlinear effects, such as geometric, material, and/or contact
nonlinearities, are included by updating the stiffness matrix.
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… Introduction
Training Manual
• Transient structural analysis encompasses static structural analysis
and rigid dynamic analysis, and it allows for all types of Connections,
Loads, and Supports.
• However, one of the important considerations of performing transient
structural analysis is the time step size:
– The time step should be small enough to correctly describe the timevarying loads
– The time step size controls the accuracy of capturing the dynamic
response. Hence, running a preliminary modal analysis is suggested in
Section B.
– The time step size also controls the accuracy and convergence behavior
of nonlinear systems. Background information on the Newton-Raphson
method is presented in Section C.
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B. Preliminary Modal Analysis
Training Manual
• While transient structural analyses use automatic time-stepping,
proper selection of the initial, minimum, and maximum time steps is
important to represent the dynamic response accurately:
– Unlike rigid dynamic analyses which use explicit time integration,
transient structural analyses use implicit time integration. Hence, the
time steps are usually larger for transient structural analyses
– The dynamic response can be thought of as various mode shapes of the
structure being excited by a loading. The initial time step should be
based on the modes (or frequency content) of the system.
– It is recommended to use automatic time-stepping (default):
• The maximum time step can be chosen based on accuracy concerns. This
value can be defined as the same or slightly larger than the initial time step
• The minimum time step can be input to prevent Workbench Mechanical from
solving indefinitely. This minimum time step can be input as 1/100 or 1/1000 of
the initial time step
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… Preliminary Modal Analysis
Training Manual
• A general suggestion for selection of the initial time step is to use the
following equation:
tinitial
1
20 f response
where fresponse is the frequency of the highest mode of interest
• In order to determine the highest mode of interest, a preliminary
modal analysis should be performed prior to the transient structural
analysis
– In this way, the user can determine what the mode shapes of the
structure are (i.e., how the structure may respond dynamically)
– The user can also then determine the value of fresponse
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… Preliminary Modal Analysis
Training Manual
Points of Consideration:
• The automatic time-stepping algorithm will increase or decrease the
size of the time step during the course of the analysis based on the
calculated response frequency.
– Automatic time-stepping algorithm still relies on reasonable values of
initial, minimum, and maximum time steps
– If the minimum time step is being used, that may indicate that the initial
time step size was too large. The user can plot the time step size by
selecting “Solution Output: Time Increment” from the Details view of the
Solution Information branch
• When performing a modal analysis to determine an appropriate
response frequency value, it is not sufficient to request a certain
number of modes, then to use the maximum frequency. It is a good
idea to examine the various mode shapes to determine which
frequency may be the highest mode of interest contributing to the
response of the structure.
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C. Including Nonlinearities
Training Manual
• There are several sources of nonlinear behavior, and a transient
structural analysis may often include nonlinearities:
– Geometric nonlinearities: If a structure
experiences large deformations, its
changing geometric configuration can
cause nonlinear behavior.
– Material nonlinearities: A nonlinear stress-strain
relationship, such as metal plasticity shown on
the right, is another source of nonlinearities.
– Contact: Include effects of contact is a type
of “changing status” nonlinearity, where an
abrupt change in stiffness may occur when
bodies come in or out of contact with each other.
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… Including Nonlinearities
Training Manual
• In a linear analysis, the applied force F and
displacement x of the system are related such
that doubling the force would double the
displacement, stresses, and strains
F
K
– This assumes that the change in the original and
final deformed shapes is negligible since the same
stiffness matrix [K] is used
x
• In a nonlinear analysis, the relationship between
the applied force F and displacement x is not
known beforehand
– As the geometry undergoes deformation, so too,
does the stiffness matrix [K] change
– The Newton-Raphson method needs to be
implemented to solve nonlinear problems
F
x
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… Including Nonlinearities
Training Manual
• Nonlinear analyses require several solution iterations:
– The actual relationship between applied load and deformation (dotted
green line below) is not known a priori
– The Newton-Raphson method, which can be thought of as a series of
linear approximations with corrections, is performed (solid blue lines)
• The load Fa is applied to the structure. Based on the new deformed shape,
internal force F1 is calculated. If Fa ≠F1 then the system is not in equilibrium. A
new stiffness matrix [K] (slope of blue line) is calculated based on the current
conditions.
• This process is repeated until Fa =Fi for iteration i, at which point the solution is
said to be converged
• Oftentimes, the applied load Fa must be
split into smaller increments in order for
convergence to occur. Hence, for a ramped
load, a smaller time step may be needed
to ensure convergence
Fa
3
2
F1
1
x1
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… Including Nonlinearities
Training Manual
• As shown from the previous slides, the time step size will also have
an influence on nonlinear analyses:
– The time step size should be small enough to allow the Newton-Raphson
method to obtain force equilibrium (convergence)
– The user may also need to specify the initial, minimum, and maximum
timesteps based on nonlinear considerations
• Usually, the dynamic considerations for picking a time step size as
discussed in Section B is sufficient.
– Since Workbench Mechanical only uses one set of time steps, resolving
the dynamic response often provides a small enough time step to resolve
nonlinear effects as well.
– Determination of the time step size based on nonlinear considerations is
often not as straightforward as choosing the dynamic time step size.
Hence, the user may rely on automatic time-stepping algorithm to ensure
convergence and accuracy.
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… Including Nonlinearities
Training Manual
• The automatic time-stepping algorithm takes into account the
following nonlinear effects:
– If force equilibrium (or some other convergence criterion) is not satisfied,
bisection occurs
– If an element has excessive distortion, bisection occurs
– If the maximum plastic strain increment exceeds 15%, bisection occurs
– Optional: if contact status changes abruptly, bisection occurs
• Bisection is part of the automatic time-stepping algorithm, when the
solver goes back to the previously converged solution at time ti and
uses a smaller time increment ti.
– Bisections provide an automated means to solve nonlinear problems
more accurately or to overcome convergence difficulties.
– Note, however, that bisections result in wasted solver time since the
solution returns to the previously converged solution and tries again with
a smaller time step. Hence, choosing the right initial and maximum time
step can minimize the number of bisections that occur
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… Including Nonlinearities
Training Manual
• By default, large deformation effects and automatic time-stepping will
be active:
– The user does not need to do anything special to account for
nonlinearities.
• However, as noted before, if nonlinear effects dominate, the time step size may
be dictated by nonlinear considerations rather than dynamic concerns.
• “Large Deflection” can be toggled in the Details view of the “Analysis Settings”
branch
– If the user wants to turn on time step size checks based on contact status,
this can be done in with “Time Step Controls” in the Details view of a
given contact region.
• Using this option may decrease the time step to ensure correct momentum
transfer between parts in impact-type of situations
• Note, however, that the time step may become excessively small, so this is not
recommended in general, especially for preliminary analyses
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Procedure:
Transient
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E. Part Specification
Training Manual
• In a transient structural analysis, parts may be rigid or flexible:
– Under the “Geometry” branch, the “Stiffness Behavior” can be toggled
from “Flexible” to “Rigid” on a per-part basis
– Rigid and flexible parts can co-exist in the same model
• Consideration for flexible parts are the same as in static analyses:
– Specify appropriate material properties, such as density, Young’s
Modulus, and Poisson’s ratio
– Nonlinear materials, such as plasticity or hyperelasticity, can also be
included
• For rigid parts, the following apply:
– Line bodies cannot be set to rigid
– Multibody parts must have all bodies set to rigid
– Density is the only material property needed to
calculate mass properties. All other material
specifications will be ignored.
– An “Inertial Coordinate System” will automatically
be defined at the centroid of the part
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… Part Specification
Training Manual
• For flexible bodies, the mesh density is based on the following:
– The mesh should be fine enough to capture the mode shapes of the
structure (dynamic response)
– If stresses and strains are of interest, the mesh should be fine enough to
capture these gradients accurately
• For rigid bodies, no mesh is produced
– Rigid bodies are rigid, so no
stresses, strains, or relative
deformation is calculated.
Hence, no mesh is required
– Internally, rigid bodies are
represented as point masses
located at the center of its
“Inertial Coordinate System”
On the figure on the right, one can
see flexible bodies (meshed) and
rigid bodies (not meshed) in the
same model.
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Assembly shown here is from an Autodesk Inventor sample model
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F. Nonlinear Materials
Training Manual
• For flexible bodies, nonlinear materials may be defined:
– Metal plasticity:
• Define Young’s modulus and Poisson’s ratio
• Select either isotropic or kinematic hardening law and either bilinear or
multilinear representation of stress-strain curve
– For multilinear stress-strain curve, remember that values should be logarithmic plastic
strain vs. true stress
– Hyperelasticity:
• Select a hyperelastic model based on strain invariants (neo-Hookean,
Polynomial, Mooney-Rivlin, or Yeoh) or principal stretch (Ogden):
– If material constants are not known, enter test data, then select hyperelastic model on
which to perform curve-fit
– If material constants are known, select hyperelastic model and enter constants
• To account for inertial effects, density should also be defined for
both flexible and rigid bodies.
• Material damping, discussed in Section I, may also be input for
flexible bodies.
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G. Contact; Joints; Springs
Training Manual
• Contact, joints, or springs can be defined under the “Connections”
branch in transient structural analyses
– Contact is defined between solid and surface bodies (rigid parts must be
single body). Contact is used when parts can come in and out of contact
or if frictional effects are important.
• Nonlinear contact (rough, frictionless, frictional) may be defined for faces of
solid or surface bodies (flexible or rigid) at v12.
– Joints are defined for 3D rigid or flexible bodies only. Joints can be
defined between two bodies or from one body to ground. Joints are
meant to model mechanisms where the part(s) are connected but relative
motion is possible.
• Joints are defined faces, lines, or keypoints of 3D solid, surface, or line bodies,
both flexible and rigid.
– Springs are defined for 3D rigid or flexible bodies. Springs provide
longitudinal stiffness and damping for the scoped region(s), meant to
represent stiffness/damping effects of parts not explicitly modeled.
• Springs can be defined on vertices, edges, or faces of 3D bodies
• Defined springs cannot have zero length
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… Contact
Training Manual
• Contact regions can be defined between flexible bodies:
– Contact is useful when the contacting area is not known beforehand or if
the contacting area changes during the course of the analysis
– Any type of contact behavior (linear, nonlinear) can be specified,
including frictional effects
• Play Animation
In the animation, some
surfaces of two parts are
initially not in contact, but
as the analysis
progresses, the surfaces
come into contact, as
shown on the right,
allowing for forces to be
transmitted between the
two bodies.
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… Contact
Training Manual
• In contact, parts are prevented from penetrating into each other. The
different type of contact describe behavior in the separation and
sliding directions:
Contact Type
Bonded
No Separation
Rough
Frictionless
Frictional
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Normal Direction
Separate
no
no
yes
yes
yes
Tangential Direction
Slide
no
yes
no
yes
yes (when Ft ≥mN)
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… Contact
Training Manual
• Different contact formulations allow for establishing the mathematical
relationship between contacting solid bodies:
– For bonded and no separation contact, the contacting areas are known
beforehand based on the geometry and pinball region
• The recommended contact formulation to use is either “Pure Penalty” (default)
or “MPC”
– For rough, frictionless, and frictional contact,
the actual contacting areas are not known
a priori, so an iterative approach is required
• The recommended contact formulation to use
is “Augmented Lagrange”
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… Joints
Training Manual
• Joints can be defined between bodies or from a body to ground:
– Joints define the allowed motion (kinematic constraint) on surface(s)
– Various types of joints can be defined for flexible or rigid bodies:
• Fixed, Revolute, Cylindrical, Translational, Slot, Universal, Spherical, Planar,
or General Joints
– Definition and configuration of joints is covered in a separate training
course named “ANSYS Rigid and Flexible Dynamic Analysis”.
– Unlike rigid dynamic analysis, the actual – not relative – degrees of
freedom are specified.
The animation on the right shows
an assembly using cylindrical and
revolute joints
Assembly shown here is from an Autodesk Inventor sample model
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… Joints
Training Manual
• In transient structural analyses, the user has an additional option of
specifying the behavior of the joint:
– “Rigid” (default) behavior means that the scoped surface(s) will not
deform but be treated as rigid surface(s). This means that a scoped
cylindrical surface will remain cylindrical throughout the analysis.
– “Deformable” behavior means that while the
joint constraint is satisfied, the scoped
surface(s) are free to deform. This means that
a scoped cylindrical surface may not remain
cylindrical throughout the analysis.
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… Springs
Training Manual
• Springs can be defined between bodies or from body to ground:
– Springs define the stiffness and/or damping of surface(s)
• Refer to Section I for additional details on damping
– Springs can be defined for rigid or flexible bodies
– These are longitudinal springs, so the stiffness or damping is related to
the change in length of the spring
• The spring must not have zero length
• Springs can be defined on vertices, edges, or surfaces
• Definition and configuration of springs is covered in a separate training
course named “ANSYS Rigid and Flexible Dynamic Analysis”.
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H. Initial Conditions
Training Manual
• For a transient structural analysis, initial displacement and initial
velocity is required:
– User can define initial conditions via “Initial Condition” branch or by
using multiple Steps
• Defining initial displacement & velocity with the
“Initial Condition” object:
– Default condition is that all bodies are at rest
• No additional action needs to be taken
– If some bodies have zero initial displacement but
non-zero constant initial velocity, this can be input
• Only bodies can be specified
• Enter constant initial velocity (Cannot specify more
than one constant velocity value with this method)
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… Initial Conditions
Training Manual
• Defining initial displacement & velocity by using multiple Steps:
– This technique is required for all other situations
– Leave “Initial Conditions” to “At Rest.” For “Analysis Settings,” use 2
Steps over a small time interval:
• First Step should have very small “Step End Time” in Details view. Also,
change “Time Integration: Off” and “Auto Time Stepping: Off” only for the first
Step. Modify “Define by: Substeps” with “Number of Substeps: 1”.
– Apply a “Displacement” support with appropriate values (discussed in
next slide) in Step 1. Deactivate this “Displacement” support in Step 2.
– The idea behind such a technique is that the first Step, solved over a
small time interval t1, will provide an initial displacement & velocity
based on an imposed xinitial “Displacement” support.
v
initial
x1initial
t1
If the time interval t1 is small enough, the effect on the actual ending
time should be negligible.
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… Initial Conditions
Training Manual
– Initial displacement = 0, initial velocity ≠ 0
• Ramp a very small displacement value over a small time interval to produce the
desired initial velocity. Deactivate it for Step 2.
– Initial displacement ≠ 0, initial velocity ≠ 0
• Ramp the desired initial displacement over a time interval to produce the
desired initial velocity. Deactivate it for Step 2.
– Initial displacement ≠ 0, initial velocity = 0
• Step apply the desired initial displacement over a time interval to ensure that
initial velocity is zero. Deactivate it for Step 2, if necessary.
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I. Loads; Supports; Conditions
Training Manual
• For rigid bodies, just as in a rigid dynamic analysis, only inertial
loads, remote loads, and joint conditions are supported.
– Rigid bodies do not deform, so structural & thermal loads do not apply
• For deformable bodies, any type of load can be used:
– Inertial and structural loads
– Structural supports
– Joint (for defined joints) and thermal conditions
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… Time-Varying Loads
Training Manual
• Structural loads and joint conditions can be input as time-dependent
load histories
– When adding a Load or Joint Condition, the
magnitude can be defined as a constant,
tabular value, or function.
– The values can be entered directly in the
Workbench Mechanical GUI or entered in
the Engineering Data page
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J. Damping
Training Manual
• As noted in Section A, the equations solved for in transient structural
analyses also include a damping term
• Since the response frequency is not known in advance of running the
simulation, are only two types of damping available:
– Viscous damping
• beta damping (optionally material-dependent) or by element damping
– Numerical damping
• See Chapter 1 for more details.
• The effect of damping is cumulative. Hence, if 2% materialdependent beta damping and 3% global beta damping is defined, that
part will have 5% damping.
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K. Analysis Settings
Training Manual
• Besides damping, there are various other
options the user can set under the “Analysis
Settings” branch.
• It is important that the user specify the solution
times in the “Step Controls” section
– The “Number of Steps” controls how the load
history is divided. As noted in Section G, one
can impose initial conditions with multiple load
steps – use “Time Integration” to toggle whether
inertial effects are active for that step
– The “Step End Time” is the actual simulation
ending time for the “Current Step Number”
– The initial, minimum, and maximum timesteps
should be defined as noted in Sections B & C
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… Analysis Settings
Training Manual
• The “Solver Controls” section allows the user
to choose the equation solver, use of weak
springs, and use of large deflection effects
– Transient structural analyses may typically
involve large deformations, so “Large Deflection:
On” should be used (default behavior).
– “Output Controls” allows users to control how
frequently data is saved to the ANSYS result file.
For multiple step analyses, one can save results
only for the end of the step. Also, one can also
save results at intervals that are as evenlyspaced as possible (depending on automatic
time-stepping)
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L. Reviewing Results
Training Manual
• After completion of the solution, reviewing transient structural
analysis results typically involves the following output:
– Contour plots and animations
– Probe plots and charts
• Generating contour plots and animations are similar to other
structural analyses
– Note that the displaced position of rigid
bodies will be shown in the contour result,
but the rigid bodies will not show any
contour result for deformation, stress, or
strain since they are rigid entities
– Typically, animations are generated using
the actual result sets, not distributed sets
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… Reviewing Results
Training Manual
• Probes are useful in generating time-history charts
to understand the transient response of the system.
Some useful probe results are as follows:
– Deformation, stresses, strains, velocities, accelerations
– Force and moment reactions
– Joint, spring, and bolt pretension results
• Chart objects, based on probes, can also be added
to include in reports or as independent figures
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D. Workshop – Transient Analysis
Training Manual
• In this workshop, you will determine the dynamic response of a
caster wheel exposed to a side impact such as hitting a curb.
WS6: Transient Analysis of a Caster Wheel
Striker
Tool
Wheel
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Workshop 1:
Intro (Flywheel)
ANSYS Mechanical
Dynamics
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Workshop 1 – Introduction
Training Manual
• In this workshop, the vibration characteristics of a spinning flywheel will be
investigated.
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Workshop 1 – Project Schematic
Training Manual
• Drop a Static Structural system into the Project Schematic.
• In this system, the rotational velocity will be applied.
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Workshop 1 – Project Schematic
Training Manual
• Drop a Modal system onto the Results cell of the Static Structural system.
• In this system, the prestressed modes will be found.
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Workshop 1 – Project Schematic
Training Manual
• Drop a Harmonic Response system onto the Model cell of the Static
Structural System.
• In this system, a harmonic load will be applied to the static flywheel.
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Workshop 1 – Project Schematic
Training Manual
• Import the geometry file
– Flywheel.igs
• Edit the Model cell to open the Mechanical application.
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Workshop 1 – Preprocessing
Training Manual
• Two coordinate systems will be added to align with the center of the shaft.
• The origin of the first coordinate system can easily be located along the shaft
axis by selecting two keypoints.
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Workshop 1 – Preprocessing
Training Manual
• Duplicate the first coordinate system.
– set the type of the newly-created coordinate system to Cylindrical
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Workshop 1 – Static Preprocessing
Training Manual
• Select the symmetry surfaces and insert a Frictionless support.
– Since the geometry is 3D, a frictionless support is the same as applying a
symmetry boundary condition.
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Workshop 1 – Static Preprocessing
Training Manual
• Insert a Remote Displacement on the flywheel hub.
– select the coordinate system that aligns with the axis of the shaft
– fix the X Component, Z Component, and Rotation Y
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Workshop 1 – Static Preprocessing
Training Manual
• Insert a Rotational Velocity inertial load.
– select the coordinate system that aligns with the axis of the shaft
– set the Z component to 600 RPM
• Solve the model.
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Workshop 1 – Static Preprocessing
Training Manual
• Insert a Directional Deformation.
– set the Coordinate System to the Cylindrical Coordinate System that aligns with
the axis of the shaft
• The X-Axis orientation is now the radial component.
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Workshop 1 – Static Postprocessing
Training Manual
• Duplicate the Directional Deformation.
– set the Orientation to Y Axis
• This is now the tangential component of deformation.
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Workshop 1 – Static Postprocessing
Training Manual
• Using the cylindrical coordinate system again, insert radial and tangential
components of stress.
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Workshop 1 – Modal Postprocessing
Training Manual
• Move down to the Modal branch and Solve.
• Insert some total deformation plots to review the mode shapes.
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Workshop 1 – Harmonic Preprocessing
Training Manual
• Drag and drop the Frictionless Support and Remote Displacement from the
Static Structural branch into the Harmonic Response Branch.
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Workshop 1 – Harmonic Preprocessing
Training Manual
• Insert an Acceleration inertial load.
– set the Z component to 2 G (~20000 mm/s^2)
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Workshop 1 – Harmonic Solution Settings
Training Manual
• Modify the Analysis Settings.
– set the Range Maximum to 500 Hz
– set Cluster Results to Yes
– set Constant Damping Ratio to 5%
• Solve the model.
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Workshop 1 – Harmonic Postprocessing
Training Manual
• Insert a Deformation
Frequency Response
result on the outer surface
of the flywheel.
– set the Spatial Resolution
to Use Maximum
– set the Orientation to Z
Axis
• Make note of the
frequency and phase angle
at which the maximum
amplitude occurs.
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Workshop 1 – Harmonic Postprocessing
Training Manual
• Insert a Directional Deformation result.
– set the Orientation to Z Axis
– use the frequency and phase angle for the maximum amplitude, noted from the
previous slide (229.28 Hz @ 92.859°)
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Workshop 2A:
Modal Analysis
(Plate with a Hole)
ANSYS Mechanical
Dynamics
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Workshop 2A - Goals
Training Manual
• Our goal is to determine the first 10 natural frequencies and mode
shapes for the plate with the hole shown.
• The plate is made of Aluminum.
• Assume the plate is fully constrained at the hole.
– As if the plate is tightly bolted down at the hole.
Fixed Center
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Workshop 2A – Project Schematic
Training Manual
• From the project schematic, insert a
new Modal system.
• Import the Geometry file
– plate.iges
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Workshop 2A - Preprocessing
Training Manual
• Edit the Engineering Data cell.
– add Aluminum Alloy from the General Materials library to Engineering Data
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Workshop 2A - Preprocessing
Training Manual
• Return to the Project, and Edit the Model cell to open the Mechanical
application.
– set the plate thickness to 0.1 in
– set the plate material assignment to Aluminum Alloy
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Workshop 2A - Environment
Training Manual
• Constrain the center hole.
– highlight the Modal Branch to >Insert>Fixed Supports.
• Switch to edge selection mode as necessary
• Use Box Select, or drag single-select LMB around the hole to pick all
applicable edge segments (4 edges)..
– Click “Apply” in the Details window
– Reorient model as necessary throughout.
8
9
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Workshop 2A – Modal Solution
Training Manual
• Check the Details of Modal
Analysis Settings.
– set Max Modes to Find to 10
– set Calculate Stress “Yes”
– set Calculate Strain “Yes”
• If you just want frequencies and
shapes, you don’t need to
“calculate” stress or strain. It will
save a little time to skip those
calculations.
• Solve the Modal analysis.
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Workshop 2A - Results
Training Manual
• After the modal solution is completed, review the modal shapes for each
frequency.
• Click on the Modal Solution Branch in the Tree. Then LMB on the top of the
Frequency Column in the “Tabular Data” region, and >RMB>Create Mode
Shape Results
– This will automatically insert “Total Deformation” objects in the Tree for all modes
solved.
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Workshop 2A - Results
Training Manual
• To get an overall view of the Modal results step thru (LMB) the Total
Deformation result objects for each mode.
– You can also Animate (Play & Stop) the mode from the Timeline window.
– Note: Make a note of your highest natural Frequency mode:
•
Max Indicated Freq = _________________Hz.
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Workshop 2A - Comments
Training Manual
• Remember:
– Displacements reported with mode shapes are “relative” and do not reflect the
actual max magnitudes of the displacements.
• The actual magnitudes will depend on the energy input to the system (depends on forcing
function).
• Sometimes it is challenging to visualize the true mode shape from a simple
contour plot.
– Try the Vector Display instead.
• Adjust the Vector Scale slider as desired.
• You can also animate the vector plot too.
Arrows may
be more
intuitive in
some cases.
Contour
Plot.
Difficult to
determine
deformation
directions
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Vector
Plot
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Workshop 2B:
Modal Analysis
(Model Airplane Wing)
ANSYS Mechanical
Dynamics
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Workshop 2B - Goals
Training Manual
• Our goal is to determine the first 5 natural frequencies and mode
shapes for the prestressed model airplane wing shown.
• Assume one end of the wing is fully fixed.
• The wing is made of Titanium.
Fixed End
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Workshop 2B – Project Schematic
Training Manual
• From the project schematic, insert a
new Static Structural system.
• Drop a Modal system onto the
Solution cell of the Static Structural.
• Import the Geometry file
– wing.iges
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Workshop 2B - Preprocessing
Training Manual
• Edit the Engineering Data cell.
– add Titanium Alloy from the General Materials library to Engineering Data
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Workshop 2B - Preprocessing
Training Manual
• Return to the Project, and Edit the Model cell to open the Mechanical
application.
– set the wing material assignment to Titanium Alloy
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Workshop 2B - Environment
Training Manual
• Constrain the far end of the wing.
–
–
–
–
–
On the >Static Structural branch >Insert>Fixed Supports.
Switch to face selection mode as necessary
Use LMB to pick the applicable surface.
Click “Apply” in the Details window
Use “Depth Picking” and/or reorient the model as necessary throughout.
Depth
Picking
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Workshop 2B - Environment
Training Manual
• Apply a pressure load to the underside of the wing.
–
–
–
–
On the >Static Structural branch >Insert>Pressure.
Switch to face selection mode as necessary
Use LMB to pick the applicable surface.
Click “Apply” in the Details window
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Workshop 2B – Static Solution
Training Manual
• Solve the Static Structural model.
• Review the results.
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Workshop 2B – Modal Solution
Training Manual
• Check the Details of Modal Analysis Settings
– set Max Modes to Find to 5
– set Calculate Stress to “Yes”
– set Calculate Strain to “Yes”
• Solve the Modal analysis.
5
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Workshop 2B - Results
Training Manual
• After the modal solution is completed we’d like to review the modal
shapes for each frequency.
• Click on the Modal Solution Branch in the Tree. Then LMB on the top
of the Frequency Column in the “Tabular Data” region, and
>RMB>Create Mode Shape Results
– This will automatically insert “Total Deformation” objects in the Tree for
all modes solved.
13
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Workshop 2B - Results
Training Manual
• To get an overall view of the Modal results step thru (LMB) the Total
Deformation result objects for each mode.
– Remember to Animate (Play & Stop) the mode from the Timeline
window.
• You can typically rotate the model during animation too.
– Note: Make a note of your highest natural Frequency mode:
•
Max Indicated Freq = _________________Hz.
• Experiment with the Vector Graphics and (vector) scale slider.
Animation and rotation can also be performed on Vector plots.
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Workshop 3:
Harmonic Response
(Fixed-Fixed Beam)
ANSYS Mechanical
Dynamics
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Workshop 3 - Goals
Training Manual
• Our goal is to determine the harmonic response of a fixed-fixed beam
under the influence of two harmonic forces.
– The forces represent rotating machines mounted at the “one-third” points
along the beam.
– The machines rotate at 300 to 1800 RPM.
• The Beam (3 m x 0.5 m x 25 mm) is made of Steel.
Constrain (Fix)
Both Ends
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Workshop 3 – Project Schematic
Training Manual
• From the project schematic, insert a
new Modal system.
– we will first look at the natural
frequencies and mode shapes of the
system
• Drop a Harmonic Response system
onto the Model cell of the Modal
system to share the material
properties, geometry, and mesh.
– note that this system will not use
the modes from the Modal system
• Import the Geometry file
– beam.agdb
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Workshop 3 - Preprocessing
Training Manual
• Edit the Model cell to open the Mechanical application.
– verify that the material assignment is Structural Steel
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Workshop 3 - Environment
Training Manual
• Constrain both ends of the Beam.
–
–
–
–
–
Click on the Modal Branch and >Insert>Fixed Support.
Switch to edge selection mode as necessary
Use LMB to pick the two applicable edges.
Hold <CTRL> to add to your selections
Click “Apply” in the Details window
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Workshop 3 – Modal Results
Training Manual
• Solve the Modal analysis.
• Create some Mode Shape Results to review the results.
– note that modes 1 and 2 fall between 0 and 50 Hz
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Workshop 3 - Preprocessing
Training Manual
• Drag and drop the Fixed Support
from the Modal branch to the
Harmonic Response branch.
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Workshop 3 - Environment
Training Manual
• In the Harmonic Response branch, apply one force to one edge.
–
–
–
–
–
–
There are two edges imprinted on the beam face.
Switch to Edge selection mode as necessary and >Insert>Force.
Use LMB and drag over surface to highlight to pick the applicable edge.
Click “Apply” in the Details window
In Details, change the “Defined By” to “Components” (i.e., XYZ).
Enter 250 for “Y”. Leave Phase Angle = 0
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Workshop 3 - Environment
Training Manual
• Apply another force to the other edge.
– set Y Component to 250 N
– leave Phase Angle = 0
– We will investigate the results as the phase angle between these loads
changes.
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Workshop 3 – Harmonic Response Solution
Training Manual
• Edit the Analysis Settings.
–
–
–
–
set the Range Minimum to 0 Hz
set the Range Maximum to 50 Hz
set the Solution Intervals to 50
set the Constant Damping Ratio to 2%
• Solve the Harmonic analysis.
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Workshop 3 – Results
Training Manual
• Insert a Deformation Frequency Response.
– set the scoping to all faces on the beam
– set the Spatial Resolution to Use Maximum
– set the Orientation to Y Axis
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Workshop 3 - Results
Training Manual
• You can also plot contours at specific frequencies.
• Click RMB on the solution object and >Insert>
Stress, Strain, or Deformation
– This will insert the result object(s)
– Step thru the Details for each and specify the
Geometry and other details.
– It is necessary to specify a specific frequency and
phase angle.
Contours at a specific
Frequency
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Workshop 3 – Results
Training Manual
• Return to the second harmonic force applied.
– set the Phase Angle to 90° (we will try to excite different modes)
– resolve the Harmonic Response
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Workshop 3 – Results
Training Manual
• Return once more to the second harmonic force applied.
– set the Phase Angle to 180°
– resolve the Harmonic Response
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Workshop 4:
Response Spectrum
(Suspension Bridge)
ANSYS Mechanical
Dynamics
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Workshop 4 - Goals
Training Manual
• Our goal is to determine the response of a prestressed suspension
bridge subjected to a seismic load.
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Workshop 4 – Project Schematic
Training Manual
• From the project schematic, insert a new Static Structural system.
• Drop a Modal system onto the Solution cell of the Static Structural system.
• Drop a Response Spectrum system onto the Solution cell of the Modal
system.
• Import the Geometry file
– simple_bridge.agdb
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Workshop 4 - Project Schematic
Training Manual
• Right click on Geometry, choose
Properties, then check Line Bodies
under Basic Geometry Options.
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Workshop 4 - Project Schematic
Training Manual
• Edit the Model cell to open the Mechanical application.
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Workshop 4 - Preprocessing
Training Manual
• Insert a fixed support on the vertex of all four tower foundations.
– the Modal and Response Spectrum systems will inherit this support
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Workshop 4 - Preprocessing
Training Manual
• Insert a zero-displacement constraint in the Y and Z directions on the
three outer edges at both ends of the bridge deck.
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Workshop 4 - Preprocessing
Training Manual
• Finally, insert Standard Earth Gravity from the Inertial loads toolbar
button.
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Workshop 4 – Modal Solution
Training Manual
• Change the Max Modes to Find to 10, then run the Modal solution.
– verify in Solution Information that a significant portion of the total mass
has been accounted for
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Workshop 4 - Preprocessing
Training Manual
• Insert an RS Acceleration load in the Response Spectrum branch.
Then, change Boundary Condition to All BC Supports and Direction
to Y Axis.
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Workshop 4 - Preprocessing
Training Manual
• Open the supplied seismic data from the Savannah River Earthquake,
copy the spectrum data, and paste it into the Tabular Data.
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Workshop 4 - Results
Training Manual
• Since the seismic data were supplied in units of G acceleration, insert a
Scale Factor equal to the acceleration due to gravity of the working units.
– Finally, run the solution and
insert the result item of your
choice.
– Note that the bridge deck
may need some mesh
refinement. Try changing the
mesh settings and resolving.
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Workshop 5A:
Random Vibration
(Girder Assembly)
ANSYS Mechanical
Dynamics
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Workshop 5A - Goals
Training Manual
• Our goal is to investigate the
vibration characteristics of a Girder
Assembly.
• In this workshop, we will examine
the displacements and stresses in a
steel assembly due to an
acceleration spectrum.
• A PSD spectrum can be specified
via Acceleration, Velocity, or
Displacement.
A2
Acceleration
– The spectrum will typically be
measured during physical tests or
documented in a written
specification relating to the system
or component.
– The data points can be entered for
each Freq & Amplitude, or a function
can be entered.
A3
A1
A4
F1
F2
F3
F4
Frequency
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Workshop 5A – Project Schematic
Training Manual
• From the project schematic, insert a
new Modal system.
• Drop a Random Vibration system
onto the Solution cell of the Modal
system.
• Import the Geometry file
– girder.agdb
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Workshop 5A – Preprocessing Thickness
Training Manual
• The first preprocessing task is to
specify the thickness of all the
surfaces.
• Select all the bodies to assign a
uniform thickness
– LMB to select the top Body in the
Part list.
– Hold <shift> and LMB on the last
Surface Body.
• Note: By highlighting “all”, we can
set the thickness on the first one, and
the same thickness gets assigned to
all of them.
– Left click in the thickness field and
set the Thickness = 0.5 in
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Workshop 5A – Preprocessing Mesh Size
Training Manual
• The assembly consists of multiple
slender bodies plus a large flat Roof
plate.
• We want to specify a relatively fine
mesh size on the slender members
but a larger element up top.
–
–
–
–
–
–
select the roof body
Mesh >Insert >Sizing
set Element Size to 2 in
select all other bodies
Mesh >Insert >Sizing
set Element Size to 4 in
• Preview the mesh,
>Mesh>Generate Mesh
– If desired, repeat the steps above to
increase or decrease element sizes
as desired to enhance the model or
reduce CPU time.
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Workshop 5A - Environment
Training Manual
• For the lower edges of the truss,
highlight the “Modal” branch in
the Outline and >Insert >Fixed
Supports.
• Switch to edge selection mode
as necessary
– Reorient model as necessary
throughout.
– Using the “Extend to Limits”
feature is probably the most
convenient.
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Workshop 5A - Environment
Training Manual
• For the PSD Base Excitation loads,
at the Random Vibration Branch,
>Insert>PSD Acceleration
– set Boundary Condition to Fixed
Support
– this is a reference to the Fixed
Support in the modal Branch
Acceleration
A2
A3
A1
A4
F1
F2
F3
F4
Frequency
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Workshop 5A – PSD Loads
Training Manual
• Enter the following tabular data for the PSD Acceleration load
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Frequency [Hz]
Acceleration [(in/s^2)^2/Hz]
5
150
20
200
30
200
45
100
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Workshop 5A – Modal Results
Training Manual
• After the solution is completed you
can review the (precursor) modal
shapes for each frequency.
– In the Outline Tree pertaining to
Modal, click on Solution (within
the Modal branch)
– Click on the Modal Solution Branch
in the Tree. Then LMB on the top
of the Frequency Column in the
“Tabular Data” region, and
>RMB>Create Mode Shape Results
– This will insert “Total Deformation”
objects in the Tree for all modes
solved.
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Workshop 5A – Random Vibration Results
Training Manual
• Now review Random Vibration
results.
• Due to the applied spectrum, you
can >Insert
– Deformations
– Strains
– Stresses
• >Insert>Deformation>Directional
– Specify the Z “Orientation”
direction in the Details Pane
• >Insert>Strain>Normal
– For instance, specify Y
“Orientation” in the Details Pane
• >Insert>Stress>Equivalent (von
Mises)
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Workshop 5A - Comments
Training Manual
• Review the evaluated results.
• Remember:
– Modal displacements reported
with mode shapes are
“relative” and do not reflect
the actual max magnitudes of
the displacements.
– The PSD simulation generates
statistically “Probable”
resultant magnitudes that
depend on the energy input
magnitude and spectrum
applied to the system.
• The Damping data also plays a
roll in the magnitude of the
response.
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Workshop 6A:
Transient
(Caster Wheel Test)
ANSYS Mechanical
Dynamics
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Workshop 6A - Goals
Training Manual
• Our goal is to determine the
dynamic response of a caster wheel
exposed to a side impact such as
hitting a curb.
• This may be simulated in a physical
test by dropping a heavy Striker
Tool on the side of the wheel.
– The dropped weight represents side
impact on the wheel.
Striker
Tool
• The Wheel and Striker Tool are
made of Steel.
– Assume the far face of the
Wheel/Axle is constrained.
– Assume the sides of the Striker are
constrained to slide up and down
vertical rails.
– Assume a damping ratio of 0.02 (i.e.
2%)
Wheel
Constrain End
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Workshop 6A – Project Schematic
Training Manual
• From the project schematic, insert a
new Transient Structural system.
• Import the Geometry file
– caster_test2.agdb
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Workshop 6A - Preprocessing
Training Manual
• Edit the Model cell to open the Mechanical application.
– verify that the material assignment is Structural Steel
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Workshop 6A - Preprocessing
Training Manual
• Suppress the upper Striker.
– Expand the geometry Branch, and
determine which part is the upper
Striker. >RMB>Suppress Body
• We will incorporate the lower Striker
in the simulation only.
• We will apply an initial velocity to the
lower Striker to account for it’s
momentum due to the drop height &
force.
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Workshop 6A - Preprocessing
Training Manual
• Define the contact between the
bottom of the Striker Tool and the
top Edge of the Caster Wheel
– LMB on >Connections in the
Outline Tree.
– >Insert>Manual Contact Region
– Use Face select
– Change “Update Stiffness” to “Each
Equilibrium Iteration”
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Workshop 6A - Environment
Training Manual
• Apply constraints on the end
of the bore to oppose loads on
the wheel.
– Within the Flexible Dynamic
Branch >Insert>Fixed
Support
– Use Face Select, LMB and
pick four annular surfaces on
the bottom of the axle hole.
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Workshop 6A - Environment
Training Manual
• The Striker Tool is guided on rails
so it can only travel up and down
when dropped on the wheel.
– >Insert>Frictionless Support
– Use LMB and pick all four sides of
the Striker Tool block.
– Note: The “four sides” of the block
may consist of more than “four”
total faces depending on how the
(CAD) geometry was originally
generated.
a Face
a Face
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Workshop 6A - Environment
Training Manual
• Apply a gravity inertial load
– RMB >Insert>Standard Earth
Gravity to account for weight
(mass) and to accelerate the
Striker downward towards the
Wheel.
– In the Details window, change
the Direction in this case to +X
(look at the XYZ Triad to
understand global orientation)
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Workshop 6A - Environment
Training Manual
• Apply an initial velocity on the Striker.
–
–
–
–
–
Change “At Rest” to “Constant Velocity”
Use Body Select and pick and >Apply the Striker Part.
Change the Direction “Defined By” to “Components”
Enter 10 m/s for “X”
initial velocity is assigned to the picked Striker but not
the Caster Wheel
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Workshop 6A – Solution Settings
Training Manual
• Check on >Analysis Settings in the
Outline Tree
– define the analysis settings in the
“time domain”
– Verify “1” for Number of Steps
– Verify “1” for Current Step Number
– Verify “0.001” for Step end time
– Enter “0.0001” for Initial Time Step
– Enter “3e-5” for Minimum Time Step
– Enter “2e-4” for Maximum Time Step
• Solve the Transient analysis.
…it may take some hand calculations and/or
trial & error to find values that are appropriate
for the scale and severity of your non-linear
problem.
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Workshop 6A - Results
Training Manual
• After the Solution is completed review the results.
• Very important in many problems like this…
– Set Result Scale to “ 1.0 (True Scale) “
• >Insert additional solution objects of interest
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Workshop 6A - Results
Training Manual
• To get an overall view of the
Dynamic (transient) results step
thru the TimeLine for each result
plot of interest.
– Evaluate any objects that have lost
their Green Checkmark (possibly
because the Display time has
changed due to changes in the
Timeline.
– Remember to Animate (Play &
Stop) the mode from the Timeline
window.
• You can typically rotate the model
during animation too.
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If time permits, make a note of your results, and
>Insert>Sizing (at the mesh object in the outline)
and enter a smaller “Element Size” (refer to the
Graphics Ruler). Then >Solve again and compare
results.
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