Fundamentals of Structural Dynamics -...

Unrestricted Siemens AG 2013 All rights reserved. Smarter decisions, better products.

Fundamentals of Structural Dynamics

11-11-2013

Unrestricted Siemens AG 2013 All rights reserved.

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

http://www.lmsintl.com/test/testXpress-analyzer/throughput-recorder-and-analyzerhttp://www.lmsintl.com/download.asp?id=F96A8CB8-0D3B-4509-9384-5EBCD5C84574http://www.lmsintl.com/testing/rotating-machinery/time-data-acquisition-processing


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

http://www.lmsintl.com/testing/rotating-machinery/optionshttp://www.lmsintl.com/simulation/powertrain-motionhttp://www.lmsintl.com/testing/rotating-machinery/optionshttp://www.lmsintl.com/simulation/powertrain-motion

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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 Drivers &

Passengers 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


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

f = 0.4 f = 1.01 f =1.6 Frequency

Ampl

itude

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 kmc

2


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 systems 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 systems 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 (/) (%) 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


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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 (%) 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 its 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)

nk

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?


Experimental Modal Acquisition and Analysis


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


Understanding leakage and windows

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Joseph did help us a lot

Joseph Fourier (1768 - 1830)

Thorie analytique de la chaleur (1822)

Fouriers 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


44

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What is Leakage?

When the spectral content of your signal does not correspond to an available spectral line


45

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


48

Are these signals the same?

YES!

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T T = N t


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


50

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


51

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How can we minimize the effects of leakage?


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


53

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Windows distort the amplitude and total energy content of the data.


54

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


55

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Amplitude Errors


56

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Energy Errors


57

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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.


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


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


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)


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)


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*

*

)(

11-11-2013



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


Polymax MDOF Curve Fitting

11-11-2013



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


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

/s2)

/N

)

4.00 20.00 LinearHz

Hz

-180.00

180.00

Phas

e

Multiple Coherence FRFs

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LSCE

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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

/s2)

/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


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 fs s s s s s s f 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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http://www.google.com/url?sa=i&rct=j&q=big+mac&source=images&cd=&cad=rja&docid=iUXaGWc3t1aCPM&tbnid=KcUf6cfH-OwIBM:&ved=0CAUQjRw&url=http%3A%2F%2Fkaye-themill.blogspot.com%2F2012%2F01%2Fmcdonalds-big-mac-epiphany_02.html&ei=NJxJUd3ECIHVPOa7gfgG&psig=AFQjCNErETkkWLgmnLcMHsEVCcw3YDuRmA&ust=1363865006933026

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IS THIS A GOOD MAC?


Advanced Processing and Analysis Techniques


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 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

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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

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Relative Frequency Difference plot shows:

Small frequency differences

< 6% for modes 1-9

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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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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 its 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

Fundamentals of Structural Dynamics -...

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