Southern Taiwan University
Department of Mechanical Engineering
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Final Project of Vibrations for Precision Machinery
Modal Testing and Analysis of
Cantilever Beam
Professor
副教授 王永鵬
Team Members:
1. Dang Vu Hoang
2. 葉孟松
I.D: M991Y213
I.D: M9910224
June 14th, 2011
Abstract
In this report, we proceeded to do the experiment “Modal Testing and Analysis of Cantilever
Beam” using Impact Hammer modal testing.
Firstly we measure displacement of a node when we put force on difference node of a Clampedfree beam, after this the signal from transducers will send to portable pulse analyzer to get
displacement, force and frequency response in time domain .
Collect these data to import to modal analysis software. After model analysis we get nature
frequency and damping factor of guinea-pig.
Base on the result we can fully understand about vibration material especially relationship
between transfer function and modal vector, natural frequency and damping factor another hand
we got ideal how to apply modal testing in industry.
Abstract
Table of Content
1
Introduction
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2
Introduce the testing structure and its possible applications in industry.
Describe the objective of the testing and analysis.
Modal Testing
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Describe the purpose of modal testing.
2.1 Testing Equipment
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List the testing equipment including the name, brand, model number, sensitivity of
transducer …etc.
2.2 Setup of Measurement System
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Describe the connection of the measurement system.
Identify the locations at which the transducer is placed and impulse force is applied.
2.3 Testing Procedure and Parameter Setup
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Describe the procedure of modal testing.
Describe the values of important parameters for FFT analyzer.
2.4 Testing Results
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3
List testing results you obtain and your comments.
Show time domain plots including excitation and response.
Modal Analysis
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Describe the purpose of modal analysis.
3.1 Analysis Software

Describe the name and version of the Modal Analysis Software that you use.
3.2 Structure Model
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Show the plots of your structure.
3.3 Analysis Procedure and Parameter Setup
3.4 Analysis Results
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List all modal parameters and show the corresponding mode shape.
Your comments
4
Conclusions
5
References
1. Introduction
Introduce the testing structure and its possible applications in industry: With testing structure we
will know the characteristic of structure (such as natural frequency and damping factor…). So
testing structure applies to understand property of Car model, civil structure (Building. Tower
etc…), machinery model …
Describe the objective of the testing and analysis: Objective of the testing and analysis help us
understood the relationship between force impulse, displacement, nature frequency,
damping…etc.
2. Modal Testing
Describe the purpose of modal testing: So far we know the equation:
And matrix transfer function [H] is symmetric and scaling of {ω} r (Modal vector) so we just
need to measure displacement of one node when we put force to every node. That means we just
need to calculate one row or one column of [H]. After this we find the modal vector so that can
find the nature frequency. This is main purpose of modal testing. We don’t need to measure all
nodes but still get the result. And we will do the test base on this ideal
2.1.
Testing Equipment
List the testing equipment including the name, brand, model number, sensitivity of
transducer…etc
a.
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Modal Testing Hammer
Brand PCB PIEZOTRONICS.
Model Number: 086C03.
Voltage Sensitivity: 10 mV/lb, 2.25 mV/N ±15%.
Measurement Range (for ±5V output ±500bf peak, ±2200N peak.
Frequency Range: -10 dB.
Sensing Element/Sealing, material/type Quartz/Epoxy
Hammer Mass: 0.34lb = 0.16kg
Head Diameter: 0.62in = 1.57cm
Tip Diameter: 0.25in = 0.63cm
Hammer Length: 8.5in = 21.6cm
Electrical connector: type/location: BNC/Bottom of Handle
Figure 1: Model testing hammer
b. Dynamic Signal Analyzer
Figure 2. The Dynamic Frequency analyzer
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c.
Brand BK Bruel Kjaer
Model Number: Type 7533 LAN Interface Module
Type: 3109 4/2-ch. Input\Output Module
Computer
Brand: Acer Travel Mate 525 TE
CPU: Intel Pentium III 542 MHz
RAM: 128 MB
HD: 10 G
Weight: 2.1-2.5 kg
Screen Size: 12.1-13 in
d. Accelerometer sensor
Figure 3. Accelerometer sensor
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e.
Brand: PCB (PIEZOTRONICS)
Model Number: 352C65
Voltage Sensitivity: 100 mV/g, 10.2 mV/(ms-2)±10%.
Measurement Range: for ±5V: output ± 50 g peak, ± 491 ms-2 peak
Frequency Range (±10%): 0.3 to 12000 Hz
Sensing Element/Sealing: material/geometry Ceramic/Shear
Housing: material/sealing Titanium/Welded Hermetic
Size (hex x height): [0.31 x 0.42in] = [7.9 x 10.7mm].
Weight: 0.070oz = 2.0gm
Power supply
Figure 4. The Signal conditioner
This experiment used a PC with Window NT system and Dynamic analysis software. A wire
is connected between the transducers with the Hardware and LAN cable, and to connect the
hardware with PC.
3. Setup of Measurement System
Describe the connection of the measurement system:
Signal from transducer will send to the signal conditioner by special cable. Signal will be
improve quality and filtered by amplifier in Signal conditioner. After this signal will be send to
pulse portable system. Signal will be processed in this hardware and send to PC to analysis by
the LAN Cable.
Figure 5. The system connection
Identify the locations at which the transducer is placed and impulse force is applied.
The transducers are placed in the Clamp- Free beam. The beam is separated to 9 nodes (from
0 to 8). The accelerometer is placed in note 8 and force transducer is measured for we put from
node 1 to node 8. Every signal will be collected by transducer and sent to Signal conditioner.
Figure 6. Cantilever beam experiment.
3.1.
Testing Procedure and Parameter Setup
a.
The procedure of modal testing:
 Impact Hammer：
Configuration Organizer：
Excitation：Select Transducer
Response：Select Transducer
Figure 7. Configuration organizer
 Measurement：
Signal：
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Excitation → Channel → Max Peak Input
Response → Channel → Max Peak Input
Setup ：
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Figure 8. Measurement Organizer - signal
Multi-buffer l.
Trigger
Figure 9. Measurement Organizer - setup
FFT Analyzer：
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Input → Time weighting → window → Transient
Output → Time weighting → window → Exponential
Figure 10. FFT analyzer – input and output set up
Function Organizer：
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b.
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Time Group → Time（excitation）
Time Group → Time（Response）
Multi Buffer - export FRFs to Modal
The values of important parameters for FFT analyzer
Excitation：
Max Peak Input ＝ 223.6 mV
Shift ＝ 1 ms
Length ＝ 3 ms
Time weighting ＝ Transient
The Max Peak Input is set at small value to enable the measurement in certain range of
impulse force and also to prevent overload. The transient window is chosen. When impulse force
is applied, some noises will appear and it will take some time to decrease to zero. The
importance of the window is makes sure that noise from previous excitation will not influence
the next excitation.
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Response：
Max Peak Input ＝ 7 V
Shift ＝ 1 ms
Tau ＝ 150 ms
Time weighting ＝ Exponential
Setup：
Multi-buffer 1 → Size ＝ 8
Trigger → Time delay ＝ -1ms
FFT Analyzer：
Max frequency ＝ 3200 Hz
Sample ＝ 3200
2.4 Test result
List testing results you obtain and your comments: Response (accelerometer) in time domain
(FFT analyzer), Excitation (Force hammer) in time domain (FFT analyzer), Frequency response
(FFT analyzer).
The result we got from testing similar with theoretical result. When we do the testing, we
have pay attention in put force step because some time you may put double hit. If you did, you
will get wrong data.
In frequency response in time domain, from each mode we will see that has the maximum
magnitude at nature frequency of this mode. So base on series peak of each mode we can find
natural frequency.
Figure 14. Plot of excitation
Figure 15. Time domain plot of excitation respond
Figure 16. Screen shoot of frequency respond
Modal Analysis
Describe the purpose of modal analysis
Modal analysis is the step after modal testing. The main purpose of modal analysis is study
of the dynamic properties of structures – natural/resonant frequency, damping and mode shapes –
under vibration excitation. Modal analysis can be used for the following purposes:
 Troubleshooting
Direct insight into the root cause of vibration problems
 Find structural flexibility properties quickly
Monitor incremental structural changes
 Design optimization
Design according to noise and vibration targets
Enhance performance and reduce component and overall vibration
Fast, test-based evaluation of redesign for dynamics
 Diagnostics and health monitoring
Confirm product quality from the production line and in the field
3.1 Analysis software
Describe the name and version of the Modal Analysis Software that you use
The name and version of the Modal Analysis is ME’ScopeVES Version 2.0.0.26 (Vibration
Technology, Inc.). With ME’ScopeVES (Visual Engineering Series) you can visualize, analyze,
and document the static and dynamic behavior of machinery and structure.
ME’ScopeVES can import all popular types of time or frequency domain measurement
waveform and it also can build 3-D structure of testing model. After that it can measure
reasonable vibration on machinery (or Nature frequency) and Visualize 3-D vibration base on
each mode (each nature frequency) so we can fully understand characterize of structure
3.2 Structure Model
Show the plots of your structure.
The structure is simplified as line element with 8 points and 1 fixed point as shown in
figure 12. The distance between each point is 6 centimeters.
3.3 Analysis Procedure and Parameter Setup
The analysis is done by following this procedures and set up parameters:
 Build new structure:
From the main window select File\New \Structure and then Generate Structure Window
will appears.
 Set up the unit:
Under Structure Window select File\ Options\ Unit Tab, and then set the unit as follow:
Mass: Units\Kilogram (Kg)
Force: Units\Newton (N)
Length: Units\Meter (m)
 Draw the Structure
It is can be done by 2 methods:
Manually
Under Structure Window select Points, Lines, Surfaces item and then draw in the drawing area.
Using drawing assistant
Under Structure Window select Draw\Drawing Assistant and then edit the fill out any
requirement data to build new structure. There is 8 lines with 6 cm/line.
 Numbering Points: Under Structure Window select Draw\Points\Number Points. And then
select each points that want to be numbered by clicking in the nearby of the point.
 Import data
Under Main window select File\Import \Data Block, select the data want to be used. And then
Data block window will appears. Under Data Block Window select Edit DOF\Roving DOF and
set this parameter
Start= 1X ; Increment= 1X ; after 1 M#S
 Connect Data to the Structure
It can be done on two ways:
a. Under Data Block Window
Select Tools\Assign M#s?
Click on a point and direction to assign the M#s
b. Under Structure Window
Select Draw\ Assign M#s
 Edit Animation Equations
Select Structure Window select Edit\Animation Equations, on Vector tab set the parameter
as follow:
Point 1~8: (X, Y, Z) Interpolated& Points 9: (X, Y, Z) Fixed
 Compute the Mode Shapes
Under Data Block Window Select Mod\Modal Parameters
Analysis Results
List all modal parameters and show the corresponding mode shape. Analysis results
including natural frequency for first 8 modes, damping factor and damping ratio shown in shape
table in figure 19. Modes 1-8 were computed directly after 8th step of experiment procedure. But
as mentioned before for low frequency where the first mode usually exists, the peak cannot be
observed clearly. Therefore, in order to find the first mode curve fitting should be done again
especially in the small range that is considered that the first mode exist.
Shape 1: 17.832Hz
Shape 2 : 123.282Hz
Shape 3: 333.312Hz
Shape 6: 1074.853Hz
Shape 5: 562.865Hz
Shape 1: 123.986Hz
Shape 2: 341.459Hz
Shape 4:1074.667Hz
Shape 3: 652.789Hz
Shape 5: 1206.538Hz
 The comments
We have the result included frequencies, damping and residue magnitude.
+ Shape 6, shape 7 and shape8 show the good performance represent for
mode6, mode7 and mode8.
+ Shape 1, shape 2 and shape 3 the result are not very good when compare
with the theoretical result. However, they all are acceptable.
The result that we got from the experiment could not perform completely the
same the theoretical result.
We have difference because of environment and characterize of material we
choose (general steel), and error when we did the test (such as when we
putted force to node, we didn’t put exactly, just around node and error from
testing equipments)
4. Conclusions
 Practiced model testing we fully understood the relationship between nature
frequency of model testing, modal vector and transfer function. We also
know how to test a model to characterize model’s modal property such as
how to setup trigger, excitation, response,… and how apply it on real life, so
we can think about ideal how to improve stable of structure.
 Another hand after took the test we know which node shakes the most, so we
can control the structure like when we design a model, consider where is
vibration the most so we will modified something to decrease.
 Finally in the present, modal testing is more and more efficient in design and
build everything in real life especially in industry.
5. References
[1] Vibrations: Analytical and experimental modal analysis. - Dr. Randall
J.Allemang
[2] Lecture Note
[3] ME’ scope Help
[4] Brüel & Kjær document
[5] Modal Testing – D.J Ewins, Research studies press Ltd
[6] Harris’ Shock and Vibration Hand Book-Cyril M.Harris, Allan G.Piersol
[7] Internet source