fundamentals of structural dynamics · 2019-05-21 · fundamentals of structural dynamics review...
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Fundamentals of Structural Dynamics
11-11-2013
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Page 2 Siemens PLM Software
Structural Dynamics Agenda Topics
Modal Analysis
Curve fitting, data quality checks
(MAC), mode shapes
How does my structure naturally want to move?
How to validate simulation models?
Modal Correlation
Modal Assurance Criteria, Modal
Contribution, Updating
How to characterize structural behavior?
Fundamentals
Natural Frequencies, Resonances, Damping
airair--bornebornestructurestructure--borneborne
structurestructure--borneborne
airair--bornebornestructurestructure--borneborne
structurestructure--borneborne
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Why are structural dynamics important?
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Product Development Process C
ost o
f Cha
nge
Concept Detail Drawing
Prototype Production Field Failure
Troubleshoot
Engineer
Validate
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Why identify structural resonance?
Field failure
Pains W
hat ?
Increasing speed causes: - Component breakdown
- Machine failure - Poor precision
- Inconsistent product quality …
Excessive vibration problems
Durability
Noise & Vibration problem
- Steerling wheel shake - Driver seat vibration - Noise at Driver’s &
Passenger’s Ears …
Performance/Perceived Quality
Product Certification
- Structural integrity - Ground Vibration Testing
- Reduce vibration dose value - Flutter phenomena
…
Safety
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Aircraft Flutter
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Tacoma Bridge Collapse
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Natural frequency of a traffic signal
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What is a natural frequency?
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Natural Frequency
Natural frequency is the frequency at which a system naturally vibrates once it has been forced into motion
(rad/sec)frequency naturalm
kn
ground
m
c k
x(t)
f(t)
Single Degree of Freedom System
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Natural Frequency
11 copyright LMS International - 2005
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Resonant Frequency Resonance is the buildup of large amplitude that occurs when a structure
is excited at its natural frequency
ω f = 0.4 ω f = 1.01 ω f =1.6 Frequency
Ampl
itude
ω n = 1.0
3 Single Degree of Freedom Systems with same mass, stiffness and damping
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Structural Damping
Damping is any effect that tends to reduce the oscillations in a system
21 nd km
c
2
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How do we determine the resonant behavior of a structure?
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Frequency Response Functions
FORCE
RESPONSE
Frequency Response Functions (FRFs) measure the system’s output in response to known an input signal
input
outputFRF
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Frequency Response Functions
FORCE
RESPONSE
Frequency Response Functions (FRFs) measure the system’s output in response to known an input signal
input
outputFRF
0.00 1024.00Hz
-100.00
-50.00
dBN2 /H
z
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What can an FRF tell you?
Resonant Frequency
Damping
95010 100 200 300 400 500 600 700 800150 250 350 450 550 650 750 850Hz
1.6
-0.1
1.0
0.5
0.1
0.3
0.7
1.2
1.4
Imag
g/N
1
-700e-3
Rea
lg/
N
100 200 300 400 500 600 700 800 90050 150 250 350 450 550 650 750 850
135.31
Curve 135.31 Q (/) ζ (%) Hz1.520.48
14.04 3.56g/Ng/N
Mode Shape Requires Multiple FRFs
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Quality Factor
Q-factor describes whether a system is heavily or lightly damped
12
o
ff
fQ
Half Power (3 dB) Method
21
Q
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Other Damping Terms
19 copyright LMS International - 2005
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DEMONSTRATION: Test.Lab Cursor Calculations
6015 20 30 40 5025 35 45 55Hz
0.70e-3
-0.40e-3
0.00
0.50e-3
-0.30e-3
-0.20e-3
-0.10e-3
0.10e-3
0.20e-3
0.30e-3
0.40e-3
0.60e-3
Imag
(m/s
)/N
18.44 27.19 49.69 55.63 58.75
0.10e-3
0.62e-3
0.09e-3
0.16e-3
0.09e-3
Curve 18.44 27.19 49.69 55.63 58.75 ζ (%) Hz0.10e-3 0.62e-3 0.09e-3 0.16e-3 0.09e-3 23.08 | 0.93 | 0.93 | 1.13 | 5.72 (m/s)/N
FRF (Acceleration/Force)
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FRFs determine mode shapes
1st Bending Mode
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FRFs determine mode shapes
1st Torsional Mode
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Experimental Modal Analysis The process of identifying the dynamic behavior of a system (structure) in terms of it’s modal parameters Modal parameters • Frequency • Damping • Mode Shape
Troubleshooting Simulation and prediction Optimization Diagnostics and health monitoring
ground
m
c k
x(t)
f(t)
ωn
k
m
Single Degree of Freedom System
21 nd
km
c
2
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Experimental Modal Analysis Process
0 500100 200 300 40050 150 250 350 45025Hz
0
24
10
20
4
8
1416
Ampl
itude
(m/s
2)/N
Frequency Damping
Mode Shapes
Input Input
Curve Fit to Estimate Modal Parameters
Measure the Frequency Response Functions
Response
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Fundamentals of structural dynamics review
Why are resonant frequencies important? How can I get realistic damping values? What is the significance of Frequency Response Functions and how can they help me? What can I learn from a mode shape?
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Experimental Modal Acquisition and Analysis
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Measurement Techniques
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Measurement Equipment Excitation
• Laboratory (shakers, hammer, force cell, …)
• Operational excitations (road simulation, flight simulation, wind excitation, …)
• Unusual excitations (loudspeaker, gun shot, explosion, …)
Response • (Accelerometers, Laser,…) Measurement system
• FFT analyzer (2-4 channels) • PC & data-acquisition
front-end (2-1000 channels)
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Excitation Techniques
Shaker Testing Impact Testing
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Impact Testing
Minimal equipment Easy and fast Good for wide range of structures Limited frequency range Typically: fixed response accelerations - roving impact location
Time Frequency
Inpu
t R
espo
nse
FRF
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Impact Testing
Blue Line – Hammer Input Autopower Red – Coherence Black - FRF
Correct Tip Soft Tip
Shorter impact time Wider freq range
1000 Hz 1000 Hz
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Huge Impact Test
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Exponential Window
Exponential Window for Response
• Exponential Window Increases Apparent Damping Values When Applied. • Avoid Applying The Exponential Window Unless Absolutely Necessary.
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Coherence
Coherence
Coherence is a value from 0 to 1 that shows how much of the output is really due to the input
1
0
/
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Coherence
Coherence differs from 1 in case of: • Non-Linearity • Unmeasured sources • Antinodes • Frequency range of excitation • Other noise
0.00 100.00 Hz0.00
1.00
Rea
l/
F Coherence DRV:1:+XF Coherence DRV:2:+XF Coherence ENG:1:+YF Coherence FUSL:5:+X
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Pretrigger
Pretrigger is the amount of “buffer time” measured before the impulse
Lose initial part of the input signal Use a pretrigger to avoid distorted FRF
Pretrigger
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DEMONSTRATION: Modal Impact Test
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Shaker Testing
Time Consuming to setup Control frequency range Control Force Amplitude Better for larger structures Typically fixed excitation point, multiple response points - measured in batches
Inpu
t R
espo
nse
Time Frequency
FRF
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Shaker Testing: Excitation Signals
Window Required
Burst Random
Random
Generally, Burst Random is better
No Window Needed
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Effect of not using a window on excitation signal
Frequency (Hz)
Ampl
itude
(g/N
)
Burst Random
Random
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Understanding leakage and windows
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Joseph did help us a lot …
Joseph Fourier (º1768 - †1830)
Théorie analytique de la chaleur (1822)
• Fourier’s law of heat conduction
• Analyzed in terms of infinite mathematical series
2
2
2
2
y
u
x
uk
t
u-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-4
-3
-2
-1
0
1
2
3
4
Any signal can be described as a combination of sine waves of different frequencies
Useful by-product
Copyright LMS International, 2013
43
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Fourier Transform
Transforms from Time Domain to Frequency Domain Fourier: “Any signal can be described as a unique combination of sine
waves of different frequencies and amplitudes” Complicated signals become easier to understand No information is lost when converting!
Frequency (Hz)
Time (seconds)
Amplitude
Amplitude
Amplitude
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“What is Leakage?”
When the spectral content of your signal does not correspond to an available spectral line
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1 2 3 4 5 6
Hz
5v
5 V Sine Wave - 2.5 Hz 5 V Sine Wave - 3 Hz
Hz 1f
1 2 3 4 5 6
Hz
5v
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0.00 200.0010050 15010 20 30 40 60 70 80 90 110 120 130 140 160 170 180
Hz
0.00
3.00
Ampli
tude
V
F AutoPow er Point1
Non Periodic Signals – DSP Errors (Leakage)
Smaller amplitude
Smearing of spectral content
96.00 108.00100 10598 99 101 102 103 104 106
Hz
0.20
3.00
Ampl
itude
V
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Periodic Signals
T T = N t
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48
Are these signals the same?
YES!
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T T = N t
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49
Non-Periodic Signals
Are these signals the same?
NO!
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Finite Observation – Side Effect
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Leakage
0.00 100.00 Hz
0.00
1.00
Amplit
ude
( m/s2 )
0.00 100.00 Hz
-60.00
0.00 dB( m
/s2 )
Linear scale
Log scale
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0.00 100.00 Hz
0.00
1.00
Amplit
ude
( m/s2 )
0.00 100.00 Hz
-60.00
0.00
dB( m/s2 )
Linear scale
Log scale
No Leakage
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Leakage – Amplitude Uncertainty
Periodic observation
100% of amplitude
A-periodic observation
63% of amplitude
“ Boss, this system is giving me something between 6 and 10g ”
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“How can we minimize the effects of leakage?”
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52
A: Windows
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Window Types – Specific Characteristics
Tim
e do
mai
n Fr
eq. d
omai
n
Rectangular, uniform Hanning Flat top
AKA No Window
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Windows distort the amplitude and total energy content of the data.
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Window Types – Specific Characteristics
They also smear the frequency content. This smearing cannot be corrected.
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Windows Windows limit spectral resolution
Hanning: 1.5 f Up to 15% amplitude
Flattop: 3.4 f Up to 0.02% amplitude
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Amplitude Errors
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Energy Errors
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Examples of Windows
Hanning “General Purpose”
Flattop “Single Tone Frequencies”
Uniform “No Window”
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Exponential Window
Exponential Window for Response
• Exponential Window Increases Apparent Damping Values When Applied. • Avoid Applying The Exponential Window Unless Absolutely Necessary.
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Tips for modal testing
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Boundary Conditions – What are your goals?
Real boundary conditions • Flexibility of fixtures • Added damping, stiffness, mass • Environmental Conditions
Free-free suspension In practice: almost “free-free”
• Soft spring, elastic cord • Pneumatic suspension
• Correlation with FEM •Can Obtain Rigid Body Modes •Verification of Channel Setup (Sensor Direction)
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Rigid Body Modes – Rigid Body Properties
68 copyright LMS International - 2005
Rigid body mode frequency < 10 % of first flexible mode
Free-Free Boundary Condition • Approximation of a true “Free System” (FEM) • Rigid Body Modes Are No Longer Zero – Negligible Effect on
Flexible Mode
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Boundary Conditions
Pneumatic suspension Elastic cords
Some Practical Examples – Simulating Free-Free
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Frequency Response Function - Considerations
Time invariance… • Will I get the same measurement
tomorrow? • Is the measurement repeatable?
Is the system linear?
• Different force levels can have an effect
(i.e. rubber bushing).
Does reciprocity hold true?
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Driving Point FRF
Driving Point FRF is when the excitation point equals the response point
Anti-resonances occur between every resonance Phase is combination of SDOF systems with phase information pointing in same direction At least 1 driving point necessary for modal scaling
Real
Imaginary
Magnitude
Phase
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Driving Point FRF
Selection and verification of excitation locations • Are all modes present in driving point FRF ? • At nodal point: mode is not excited • Spatially separated
Good excitation point
Bad excitation point
Measure Driving Points for a number of positions and compare FRFs
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Linearity of the FRF
3 different excitation levels
0.00 100.00 Hz1.00e-6
1.00
Log
N2
F AutoPow er FOR:1:+XF AutoPow er FOR:1:+XF AutoPow er FOR:1:+X
0.00 100.00 LinearHz
10.0e-6
0.10
Log
(g/N
)
FRF DRV:1:+X/FOR:1:+XFRF DRV:1:+X/FOR:1:+X (1)FRF DRV:1:+X/FOR:1:+X (2)
0.00 100.00 LinearHz
0.00 100.00 Hz-180.00
180.00
Phas
e°
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Measuring of Frequency Response Functions
1 2 3
1
2
3
Driving point FRFs
Excitation Degrees of Freedom (DOF)
Res
pons
e D
OF
2 1 3
Mode 1
Mode 2
Mode 3
Natural Modes of vibration
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DEMONSTRATION: Modal Impact Test
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SDOF Peak Picking
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Calculation of mode shape
1st Bending Mode
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Calculation of mode shape
1st Torsional Mode
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Experimental Modal Analysis
How do we know we have enough measurement points for our test?
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DEMONSTRATION: SDOF Peak Picking on Plate (6 points)
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Why are rigid body modes seen at high frequencies?
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Modal Assurance Criterion
1
0
.5
Modal Assurance Criterion (MAC) describes how similar the shapes are for a given mode pair using a scale of 0 to 1 (e.g. 0% to 100%)
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MAC Example
MAC = 100% correlation
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MAC Example
MAC = 0.015 (1.5% correlation)
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MAC Example
764 Hz and 385 Hz - MAC = 0.96 (96% correlation)
6 Points
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MAC Example
764 Hz and 385 Hz - MAC = 0.03 (3% correlation)
15 Points
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MAC for flat plate with 6 DOFs
Spatial Aliasing – not enough response points
1
0
.5
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MAC for flat plate with 15 DOFs
1
0
.5
No High Off Diagonal Correlations
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DEMONSTRATION: SDOF Peak Picking on Plate (15points)
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MDOF Curve Fitting
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Structure with High Modal Separation
Ampl
itude
Frequency
SDOF peak picking is only suitable for data with well-separated
modes
No influence from surrounding
modes
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Structure with Low Modal Separation
Frequency
Ampl
itude
MDOF curve fitter is required to separate
closely-spaced modes
Large influence from surrounding
modes
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Modal Parameter Estimation
Goal of modal parameter estimation • What is the model order? • How many modes to curve-fit?
Solutions • Stabilization diagram • Mode indicator functions
0.00 80.00Hz
10.0e-12
0.10
Log
(m/s
2)/N
24.09 42.72
n
i i
H
ii
i
T
ii
j
lv
j
lvH
1*
*
)(
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Modal Parameter Estimation – Assuming 1 Mode
Ampl
itude
Frequency
f1 = 50 Hz
d1 = 20 %
25 50 75
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Modal Parameter Estimation – Assuming 2 Modes
f1 = 25 Hz
d2 = 10 %
f2 = 75 Hz
d1 = 10 %
Ampl
itude
Frequency 25 50 75
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Modal Parameter Estimation – Assuming 3 Modes
f1 = 25 Hz
d2 = 5 %
f2 = 50 Hz
d1 = 5 % d3 = 5 %
f3 = 75 Hz Am
plitu
de
Frequency 25 50 75
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Modal Parameter Estimation - Stabilization Diagram
Stability : new pole : frequency : damping : all
o f d s
Compare modal parameters at current order with previous order Increase the model order until modes stabilize
Ampl
itude
Frequency
Mod
el O
rder
0
n
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DEMONSTRATION: MDOF Curve Fitting on Flat Plate
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Mode Indicator Function
Double “dip” indicates two
modes at same frequency
Mode Indicator Function (MIF) helps identify the modes for a system where multiple reference FRFs were measured commonly used to detect the presence of repeated roots
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Polymax MDOF Curve Fitting
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LSCE versus LMS PolyMAX
+Large number of responses
+Fast, efficient computation
+High damping no problem
+High modal density
+Broadband analysis
+Crystal-clear stabilization diagram
-For smaller models
-High computational load
-High damping is a problem
-High modal density
-Not for broadband analysis
-Unclear stabilization diagram
LSCE
LMS PolyMAX
Not all MDOF curve fitters are created equal !
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Modal Parameter Estimation – LSCE
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Modal Parameter Estimation – LMS PolyMAX
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DEMONSTRATION: PolyMAX Modal Analysis
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PolyMAX Validation Studies
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Validation Study of PolyMAX Algorithm
FE model of a full trimmed car body • Synthesized a set of FRFs to use for curve fitting • FRFs generated for 780 DOF / 2 references • 0.125 Hz frequency resolution • 300 modes in 0-100 Hz band, including local modes
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PolyMAX Validation Identifying Modes
Number of modes found • PolyMAX: 189/300 modes • LSCE(Time MDOF): 101/300 modes
• 0 – 60 Hz band • PolyMAX: 90/105 modes • LSCE: 70/105 modes
Possibly more modes found if more FRFs used (local modes)
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PolyMAX Validation Mode Shapes Comparison
MAC matrix LSCE (X) – FE (Y)
PolyMAX yields good correlation to higher frequency
MAC matrix PolyMAX (X) – FE (Y)
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PolyMAX Validation “Noisy” FRFs
Hz
0.05
1.00
Ampl
itude
/
F Coherence w ing:vvd:+Z/MultipleF Coherence back:vde:+Y/Multiple
4.00 20.00 Linear
Hz
10.0e-6
1.00
Log
((m/s
2)/N
)
4.00 20.00 LinearHz
Hz
-180.00
180.00
Phas
e°
Multiple Coherence FRFs
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PolyMAX Validation “Noisy” FRFs
LSCE
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PolyMAX Validation “Noisy” FRFs
LMS PolyMAX
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PolyMAX Validation FRF Synthesis with PolyMAX
4.00 20.00 Linear
Hz
1.00e-6
10.0e-3
Log
(g/N
)
4.00 20.00 LinearHz
Hz
-180.00
180.00
Phas
e°
4.00 20.00 Linear
Hz
100e-6
0.10
Log
(g/N
)
4.00 20.00 LinearHz
Hz
-180.00
180.00
Phas
e°
Left wing Back of the plane
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PolyMAX Validation Lightly-damped structures
Stabilization FRF synthesis
10.00 64.00LinearHz
10.0e-6
1.00
Log
((m/s
2)/N
)
10.00 64.00LinearHz
10.00 64.00Hz-180.00
180.00
Pha
se°
PolyMAX alleviates the need to use a different curve fitter algorithm for heavy and lightly damped structures
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#1 – Automatic Mode Expansion
Test Mesh
STL File 116 copyright LMS International - 2010
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DEMONSTRATION: Modal Expansion
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Quiz
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What can an FRF tell you?
Resonant Frequency
Damping
10.00 950.00Linear
Hz
0.0
16.0
10.0
5.0
2.03.04.0
6.07.08.09.0
11.012.013.014.0
Ampl
itude
(m/s
2)/N
10.00 950.00LinearHz
10 950100 200 300 400 500 600 700 800150 250 350 450 550 650 750 850
Hz
-180
180
Phas
e°
Mode Shape Requires Multiple FRFs
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What is this?
83785.1 LinearHz
10.4
63.3e-3
Am
plitu
deg/
lbf
o
o o
f s o
o o f o o
f s o o d o o
df s o v s o o o
ff s s s s s s f
df s v s s s f f
dd s o v s s s d f
sd s o v s s s v d
df s v v s s s d f
ss s s s s s s s d
ss s s s s s s d s
ss s s s s s s f o s
ss s s s s s s s v s
ss s s s s s s s s s
ss s s s s s s d f s
ss s s s s s s d v s
ss s s s s s s s s s
ss fs s s s s s s f s
ss s s s s s s s s s
ss os s s s s s s s o s
ss sf s s s s s d f f s o
ss sv s s s s s d s v s d
ss sv s s s s s s s v s d
ss sd s s s s s s s f s d
ss sv s s s o s s d v f s d
ss sv s s s s s s s f s d
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
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What is MAC abbreviation for?
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What is MAC abbreviation for?
Modal Assurance Criterion
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What is MAC abbreviation for?
Modal Assurance Criterion
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124 copyright LMS International - 2005
IS THIS A “GOOD” MAC?
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Advanced Processing and Analysis Techniques
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How to ensure consistency when picking modes?
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Automatic Modal Parameter Selection
Knowledge and skills of experts
Rules of Automatic Modal Parameter Selection
Observe several experienced engineers
Validated rules with benchmark study
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“LMS PolyMAX & AMPS select 173 of 233 poles in several
seconds !”
Automatic Modal Parameter Selection
Vehicle body-in-white 2 inputs and 2005 DOFs Experienced modal analysts
• Analyze in many small bands • Found 233 modes • Took a couple hours
AMPS Analyze in 4 bands Model size = 100 Found 173 modes Less than a minute
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Experimental Modal Analysis The benefits of modal analysis are:
• Identify structural dynamics properties
• Visualize how a system naturally wants to respond
• Provide insight for root-cause analysis of vibration or fatigue problems
• Determine if natural frequencies are in-line with operational frequencies
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Importance of Correlation Evaluate Design
Finite Element Simulation
Design Refinement
Durability
Loads Vibration
Acoustics
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“Old” Product Design Cycle
Product Design Process
Functional Activities
TIME
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“Modern” Product Design Process Goal
Product Design Process
Functional Activities
TIME
Simulate product
performance before
prototypes are
available
Use single
prototype & testing
for validation
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Pretest & Correlation: Process Improvement
TIME TIME
Product 1 Product 2
Pretest
Analysis
Pretest
Analysis
FE Modeling
Process Improvement
Correlation Correlation
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Virtual.Lab Pretest & Correlation: Motivation
COST ! Minimize Failures FEA accuracy degrades as mode order increases Simulation results are used for design decisions in Acoustics, NVH,
Durability, Loads, etc…
Reduce Warranty Issues Improve customer satisfaction Shorten Product Design Cycle
• Single prototype for validation
Achieve “Design Right First Time”
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DEMONSTRATION: Flat Plate
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PreTest
How many points? 6 or more?
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Correlation
Viewing mode shapes side-by-side?
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Correlation
MAC But is there something else…?
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Why the frequency difference?
All test modes higher frequency than FE Need to raise frequency of FE modes What to change…?
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Application Case: Exhaust System
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Exhaust Mode at 15 Hz
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Exhaust Mode at 15 Hz
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Exhaust Modes at 15 and 130 Hz
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Exhaust Modes at 15 and 130 Hz
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6 Exhaust Modes up to 137 Hz
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Application Case: Pretest Analysis
Step 1: Use FE model to pick some initial accelerometer locations
Supported FEA Software:
•NASTRAN •ANSYS •Abaqus •IDEAS •Elfini/GPS •Universal File Format
Initial Accel locations
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Application Case: Pretest Analysis Step 2: Use MAC to assure that accelerometer locations are sufficient to uniquely identify all modes from FEM Normal Modes Analysis
MAC: Modal Assurance Criterion A measure of how well mode shapes are correlated. In this case, the MAC diagram shows large off-diagonal terms, indicating that several modes are non-uniquely identified. Thus, more accelerometers are required to guarantee a good test.
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Application Case: Pretest Analysis Step 3: Use LMS Pretest to automatically locate additional accelerometers to meet requested MAC criterion.
• 5 accelerometers have been added to the exhaust model as shown to reach the target off-diagonal MAC of <0.15
Additional Accel’s
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Application Case: Pretest Analysis Step 3: Use LMS Pretest to automatically locate additional accelerometers to meet requested MAC criterion.
• New MAC diagram shows all modes uniquely identified. This is indicated by reduction of off- diagonal terms.
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Application Case: Pretest Analysis Step 4: Use LMS Pretest to show optimum locations of shakers or impact to excite all structural modes during the test.
• DPR (Driving Point Residue) algorithm is used to locate optimum shaker location and orientation. DPR indicates how well all modes are excited by a potential reference location.
• Practical considerations sometimes lead to selecting excitation locations other than the most optimum. In this case, several points can excite the structure sufficiently.
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Application Case: Pretest Analysis Step 5: Create wireframe geometry for Modal Test and export to LMS Test.Lab software.
• A Test.Lab project file is created containing the exhaust geometry, as well as the FE mode shapes & frequencies.
• Reduced FE modes provide the test engineer with the ability to visually check the shapes.
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Application Case: Modal Test Perform the modal test on the physical structure.
• The test engineer mounts accelerometers, and collects modal data by exciting the structure with shakers or an impact hammer in the locations as indicated by Pretest.
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Application Case: Correlation Step 1: Use the LMS Correlation Manager to import the Test and FE Models, and define correlation parameters.
Parameters: MAC threshold value for matching
of FE/Test mode pairs
Coordinate system translations and rotations
Frequency range for both FE and Test
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Application Case: Correlation Step 2: Use Correlation Tools to evaluate how well FE and Test models correlate.
Global MAC plot shows: • Good mode shape: correlation of modes 1-8
• Mode swapping between modes 11 and 13 for FE and Test models
• MAC <0.75 for modes 9-13
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Application Case: Correlation Step 2: Use Correlation Tools to evaluate how well FE and Test models correlate.
Relative Frequency Difference plot shows:
• Small frequency differences
• < 6% for modes 1-9
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Application Case: Correlation Step 2: Use Correlation Tools to evaluate how well FE and Test models correlate.
Mode Pair Table:
• Shows absolute frequency/damping differences for matching FE/Test modes
In this case:
• Good frequency correlation of modes 1-9
• Large frequency difference for mode pair 13, 11 (>14%)
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Are results close enough? Although initial inspection might lead us to assume this is good correlation, further analysis yields a different conclusion…
• Correlation of fundamental modes does not guarantee correlation throughout operating frequency band
• Higher order modes are relevant to acoustic, vibration, and durability performance – they are well within the operating frequency range
• Ignoring higher order mode correlation could lead to bad engineering decisions, for example: - Poor Exhaust Hangar locations leading to Noise and Vibration Issues - Vibration fatigue due to Engine or Road excitation at resonant frequencies
CONCLUSION: All modes in operating frequency band should be correlated!
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Application Case: Correlation Step 2: Use Correlation Tools to evaluate how well FE and Test models correlate.
MAC Contribution Display:
• Shows DOFs making most negative contribution to MAC
In this case:
• 9 DOFs can be removed to improve MAC from 85% to 95% for Mode Pair 1, 1
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Application Case: Correlation Step 3: Use LMS post processing tools to identify physical causes for poor correlation.
Post Processing Tools:
• Side by side FE/Test animation
• MAC Contribution Plots
•FRAC Plots
•CoMAC Plots
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Application Case: Correlation Step 3: Use LMS post processing tools to identify physical causes for poor correlation.
• Local stiffness differences are indicated by lower frequency of FE model for mode pair 11
• Animation provides further evidence of this
• Consideration of physical exhaust system leads engineer to consider effect of weld on this junction (ignored in the FE model)
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Application Case: Sensitivity & Updating
Sensitivity Analysis: •Sensitivity Analysis within LMS Virtual.Lab verifies that outlet junction area has dominant influence for mode pair 11
FE Model Updating:
• Manual updating
• Element thickness increased locally in weld location
• Amount of thickness increase guided by MAC and Frequency correlation
Step 4: Sensitivity Analysis and FE Model Updating
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Application Case: Sensitivity & Updating Sensitivity: Ranks the contribution of various parameters of the FE model to its modal behavior. Updating: Changing the FE model to improve it’s correlation to Test results.
Sensitivity & Updating Options: • Manual inspection & manual updating using correlation indicators
• VL Design Sensitivity Analysis & Nastran SOL200 FE Model updating
• Optimus Sensitivity Analysis and Updating with ANY FE Solver
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Application Case: Updating
• Design variables are selected from the Nastran bulk data deck.
• Shell thickness’ for the muffler, catalytic converter, pipe, and welds were selected as design variables.
• Constraints and design variables selected to avoid unrealistic changes
• Optimizer only changed the welds significantly (other parameters changed by < 1%).
Step 5: Updating
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Application Case: Results
MAC Correlation • Improved from 0.69 to 0.8
• Mode swapping eliminated
Frequency Correlation • Improved from max 15% error to 6%
• Improved from max 23 Hz error to only 8 Hz
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Application Case: Summary Pretest Analysis was used to ensure reliable Modal Test results:
• Automated wireframe creation • Optimized accelerometer/exciter locations • FE mode visualization
Correlation Analysis leveraged Modal Test results to obtain a reliable Finite Element Model
• Full frequency and mode shape correlation • Insight was provided into physical parameters of model causing
correlation issues • FE Model was Updated to improve reliability • Critical Design decisions (exhaust hangar location, fatigue life estimation,
etc.) were made based on complete and correct information
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Virtual.Lab Pretest & Correlation: Conclusions
“Design Right First Time” is critical in competitive markets • Time to Market must be accelerated • Product failure, warranty costs must be eliminated
Finite Element Models must guide product design
• Performance simulation for Acoustics, Vibration, Durability eliminates expensive, time-consuming prototypes
• Reliability of FE Models depends on modeling assumptions (weld representation, boundary conditions, etc.)
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Virtual.Lab Pretest & Correlation: Conclusions
Modal Tests must validate product designs • Reliability of test results depend upon accelerometer and shaker/impact
placement
FE/Test Correlation is Key to “Design Right First Time” • Fundamental mode correlation is not enough • Higher order modes are most difficult to correlate
LMS Virtual.Lab Pretest & Correlation Increases Reliability of FE Models and Test Results
• FE Models accurate over entire operating frequency range • Test results capturing all modes uniquely • Design decisions based on the complete and correct information