Modal Analysis

Modal Analysis and Correlation

Structural Dynamics Agenda Topics

How to characterize structural behavior?

How does my structure naturally want to move?

How to validate simulation models?

Fundamentals

Modal Analysis

Modal Correlation

Natural Frequencies, Resonances, Damping

Curve fitting, data quality checks (MAC), mode shapes

Modal Assurance Criteria, Modal Contribution, Updating

structurestructure-borne

airair-borne

structurestructure-borne

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Why are structural dynamics important?

Product Development Process Troubleshoot

Cost of Change

Validate

Engineer

Concept

Detail Drawing

Prototype

Production

Field Failure

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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?

Natural Frequency Natural frequency is the frequency at which a system naturally vibrates once it has been forced into motion f(t)

x(t) m

k

c

ground

Single Degree of Freedom System

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k n   natural frequency (rad/sec) m Siemens PLM Software

Natural Frequency

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Resonant Frequency

Amplitude

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

3 Single Degree of Freedom Systems with same mass, stiffness and damping

ω n = 1.01

Frequency

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Structural Damping Damping is any effect that tends to reduce the oscillations in a system

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c   2 km

 d  n 1  

2 Siemens PLM Software

How do we determine the resonant behavior of a structure?

Frequency Response Functions Frequency Response Functions (FRFs) measure the system’s output in response to known an input signal

o u tp u t FRF  input

RESPONSE

FORCE

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Time  Frequency

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Frequency Response Functions Frequency Response Functions (FRFs) measure the system’s output in response to known an input signal

FRF 

o u tp u t input RESPONSE

FORCE

dB

N2/Hz

-50.00

-100.00 0.00

Hz

1024.00

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What can an FRF tell you?

Mode Shape ➢ Requires Multiple FRFs

1.7 1.4 1.2 1.0

0.7 0.5 0.3 0.0 618

° Phase

Damping

g/N Amplitude

Resonant Frequency

-393 10 50

100 150 200 250 300 350 400 450 500 550 600 651 Hz

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What can an FRF tell you?

g/N Imag

1.6 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

g/N Real

-0.1 1

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-700e-3 10

50

100

150

200

250

300

350 Hz

400

450

500

550

600

651

Siemens PLM Software

Quality Factor

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Damping calculation – Active Picture 2776.18

(in/s2)/lbf Amplitude

2800.0 2400.0

2722.33 2355.74 2228.38

2000.0

Curve

Q (/) 14.15 | 17.29 | 15.85 | 19.89 | 16.30

1400.0

1381.96

1000.0

° Phase

400.0 0.0 618 75.94

84.21

60.54

71.35

49.80

-393

135.00

305.00

387.00

476.00

559.00

10

50

100

150

200

250

300

350

400

450

500

550

600

651

Hz Unrestricted © Siemens AG 2019 Page 21

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Other Damping Terms

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Mode Shape: Excitation in which a system is affected under a specific frequency. Has a particular shape in which it moves – each node moves sinusoidally with fixed phase relation to each other node

1st mode

2nd mode

3rd mode Unrestricted © Siemens AG 2019 Page 23

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Mode Shape: Excitation in which a system is affected under a specific frequency.

Has a particular shape in which it moves – each node moves sinusoidally with fixed phase relation to each other node

3rd mode Node: place where displacement is zero for a given mode shape Anti-node: position of maximum displacement Unrestricted © Siemens AG 2019 Page 24

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More interesting mode shapes…. Brake disc mode 1

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More interesting mode shapes…. Brake disc mode 2

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More interesting mode shapes…. Brake disc mode 3

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Some Math…

g/N

g/N Imag

1.6 1.0 0.5

-0.1 1 -700e-3

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10 100

200

300 400 Hz

500

651 Siemens PLM Software

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

f(t)

x(t) m

k

c

ground

Single Degree of Freedom System Unrestricted © Siemens AG 2019 Page 31

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Experimental Modal Analysis Process 24

(m/s2)/N Amplitude

20

Curve Fit to Estimate Modal Parameters

16 14 10 8 4 0 0 25 50

100

150

200

250

300

350

400

450 500

Hz

Measure the Frequency Response Functions Response

Frequency Damping Mode Shapes Input

Input

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Linearity of the FRF

N2 Log

( ) Log

0.10

g/N

1.00

AutoPow er FOR:1:+X AutoPow er FOR:1:+X AutoPow er FOR:1:+X

10.0e-6 0.00 180.00 0.00

1.00e-6

Hz Linear

100.00

Linear

100.00

Hz

° Phase

F F F

FRF DRV:1:+X/FOR:1:+X FRF DRV:1:+X/FOR:1:+X (1) FRF DRV:1:+X/FOR:1:+X (2)

-180.00 0.00

Hz

100.00

0.00

Hz

100.00

3 different excitation levels

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Measurement Techniques

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 • Data acquisition system: SCADAS (minimum 2 channels) • Processing on PC (Test.Lab) Unrestricted © Siemens AG 2019 Page 35

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Excitation Techniques

Impact Testing

Shaker Testing

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Impact Testing

Response

Minimal equipment Easy and fast Good for wide range of structures Limited frequency range

Frequency

Input

Time

FRF

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Impact Testing: Various Tips

Which tip should I use?

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Impact Testing: Various Tips

0.00

Hz

Amplitude /

dB /Hz N2

0.02

0.00

-60.00

5000.00

0.02 0.00

Hz

0.00

-60.00

5000.00

0.00

Hz

dB /Hz N2

0.02

-4.00

Amplitude /

1.00

g/N Log

5.50

Rubber Tip

-4.00 dB /Hz 2 N

1.00

g/N Log

5.50

Nylon Tip

-4.00

Amplitude /

Metal Tip

1.00

g/N Log

5.50

0.00

-60.00

5000.00

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The Right Tools for the Job

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Roving Hammer vs. Roving Accelerometer?

Any Difference? Unrestricted © Siemens AG 2019 Page 42

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1z

A2x

A2y

A2z

…

A9x

A9y

A9z

F1x F1y F1z F2x F2y

F2z

… F9x F9y F9z Unrestricted © Siemens AG 2019 Page 43

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1z

A2x

A2y

A2z

…

A9x

A9y

A9z

F1x F1y F1z F2x F2y

F2z

…

One complete Row or one complete column required to calculate mode shape

F9x F9y F9z Unrestricted © Siemens AG 2019 Page 44

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1x/F1z

A1x/F1z

A1z

A2x

A2y

A2z

…

A9x

…

A1x/F1z

A9y

A9z

F1x F1y F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

F2x F2y

F2z

… F9x F9y F9z Unrestricted © Siemens AG 2019 Page 45

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1x/F1z

A1x/F1z

A1z

A2x

A2y

A2z

…

A9x

…

A1x/F1z

A9y

A9z

F1x F1y F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

A1x/F1z

F2x F2y

F2z

…

Complete row  possible to calculate mode shape ☺

F9x F9y F9z Unrestricted © Siemens AG 2019 Page 46

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1z

A2x

A2y

A2z

…

A9x

A9y

A9z

F1x F1y F1z

A1x/F1z

A1y/F1z

A1z/F1z

A1x/F2z

A1y/F2z

A1z/F2z

A1x/F9z

A1y/F9z

A1z/F9z

F2x F2y

F2z

… F9x F9y F9z Unrestricted © Siemens AG 2019 Page 47

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Modal Test Nine Point Modal x Three Directions • Force In the ‘Z’ Direction. (One Direction) • Triaxial Accelerometer Possible Inputs and Outputs A1x

A1y

A1z

A2x

A2y

A2z

…

A9x

A9y

A9z

F1x F1y F1z

A1x/F1z

A1y/F1z

A1z/F1z

A1x/F2z

A1y/F2z

A1z/F2z

A1x/F9z

A1y/F9z

A1z/F9z

F2x F2y

F2z

Incomplete!

… F9x F9y F9z Unrestricted © Siemens AG 2019 Page 48

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Shaker Testing

Response

Time Consuming to setup Control frequency range Control Force Amplitude Better for larger structures Typically fixed excitation point, multiple response points - measured in batches

Frequency

Input

Time

FRF

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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 1.00

/ Real

Coherence differs from 1 in case of: • Non-Linearity • Unmeasured sources • Node • Frequency range of excitation • Other noise

F F F F

Coherence Coherence Coherence Coherence

DRV:1:+X DRV:2:+X ENG:1:+Y FUSL:5:+X

0.00 0.00

Hz

100.00

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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

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DEMONSTRATION: Modal Impact Test

Acquisition parameters

Joseph did help us a lot … 4 3 2 1 0 -1 -2

Joseph Fourier

-3

(º1768 - †1830)

Théorie analytique de la chaleur (1822)

-4

• Fourier’s law of heat conduction 2.5 2

  2u  2u  u k  2  2  t  x y 

1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5

Any signal can be described as a combination of sine waves of different frequencies

• Analyzed in terms of infinite mathematical series

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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 Amplitude

Amplitude

Amplitude

Time (seconds)

Frequency (Hz)

No information is lost when converting! Unrestricted © Siemens AG 2019 Page 62

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“What is leakage?”

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

f  1 Hz 5 V Sine Wave - 2.5 Hz

5 V Sine Wave - 3 Hz

5V

5V

1

2

3

4 Hz

63

5

6

1

2

3

4

5

6

Hz

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Periodic Signals

T

FFT stiches time over infinity

T = N t

Are these signals the same?

YES!

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Non-Periodic Signals

T

T = N t Are these signals the same?

NO!

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Time  Frequency

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DSP Error: Leakage

Smearing of spectral content across ALL FREQUENCIES

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Cause of leakage: Non Periodic Signals

T

T = N t

Sharp impulse  leakage

Must be removed

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Windows: Minimize Leakage

Original signal

Window function

1

x

0

= Windowed signal

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Windows: Minimize Leakage

No longer have “impulse” in signal

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How to minimize leakage? Windows.

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Window Types – Specific Characteristics Hanning

Flat top

AKA No Window

Freq. domain

Time domain

Rectangular, uniform

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Amplitude Errors

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Energy Errors

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Window Types – Specific Characteristics

Windows distort the amplitude and total energy content of the data. They also smear the frequency content. This smearing cannot be corrected. Unrestricted © Siemens AG 2019 Page 77

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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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Exponential Window for Response

• •

Exponential Window Increases Apparent Damping Values When Applied. Avoid Applying The Exponential Window Unless Absolutely Necessary.

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Driving Points

Measuring of Frequency Response Functions Excitation Degrees of Freedom (DOF)

1

2

Natural Modes of vibration

1

3

2

3

Response DOF

Mode 1

1 Mode 2

2

3 Mode 3

Driving point FRFs Unrestricted © Siemens AG 2019 Page 81

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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 Unrestricted © Siemens AG 2019 Page 83

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Driving Point Survey

FRF Point:1

Survey Location Point:1

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Driving Point Survey

FRF Point:1

FRF Point:2

Survey Location Point:2

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Driving Point Survey

FRF Point:1

FRF Point:2

FRF Point:3

Survey Location Point:3

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Driving Point Survey

FRF Point:1

FRF Point:2

FRF Point:3

FRF Point:4

Survey Location Point:4

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Driving Point Survey

FRF Point:1

FRF Point:2

FRF Point:3

FRF Point:4

FRF Point:5 Survey Location Point:5

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Driving Point Survey

FRF Point:1

FRF Point:2

Which is the FRF Point:3 appropriate excitation point? FRF Point:4

FRF Point:5 Survey Location Point:6

FRF Point:6

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Driving Point Survey

FRF Point:1

FRF Point:2

FRF Point:3

FRF Point:4

FRF Point:5 Survey Location Point:6

FRF Point:6

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Tips for modal testing

Boundary Conditions – What are your Goals?

Real boundary conditions • Flexibility of fixtures • Added damping, stiffness, mass • Environmental Conditions

“Free-free” suspension • Soft spring, elastic cord • Pneumatic suspension • Correlation with FEM •Can Obtain Rigid Body Modes

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Boundary Conditions – simulating free-free Pneumatic suspension

Elastic cords

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Boundary Conditions Some Practical Examples – Operational Conditions

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Rigid Body Modes – Rigid Body Properties Free-Free Boundary Condition • Approximation of a true “Free System” (FEM) • Rigid Body Modes Are No Longer Zero – Negligible Effect on Flexible Mode

Rigid body mode frequency < 10 % of first flexible mode Unrestricted © Siemens AG 2019 Page 95

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SDOF Peak Picking

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)

MDOF Curve Fitting

Structure with High Modal Separation

Amplitude

SDOF peak picking is only suitable for data with well-separated modes

No influence from surrounding modes

Frequency Unrestricted © Siemens AG 2019 Page 103

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Amplitude

Structure with Low Modal Separation

MDOF curve fitter is required to separate closely-spaced modes

Large influence from surrounding modes

Frequency

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Modal Parameter Estimation

Goal of modal parameter estimation

H ()   i 1

vi   liT j   i



v  l 

• What is the model order? • How many modes to curve-fit?

* i

H i * i



j  

(m/s2)/N Log

n

0.10

Solutions • Stabilization diagram • Mode indicator functions 24.09

10.0e-12 0.00

42.72 Hz

80.00

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Modal Parameter Estimation – Assume 1 Mode f1 = 50 Hz

Amplitude

d1 = 20 %

25

50

75

Frequency

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Modal Parameter Estimation – Assume 2 Modes

f2 = 75 Hz

d1 = 10 %

d2 = 10 %

Amplitude

f1 = 25 Hz

25

50

75

Frequency

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Modal Parameter Estimation – Assume 3 Modes

f2 = 50 Hz

f3 = 75 Hz

d1 = 5 %

d2 = 5 %

d3 = 5 %

Amplitude

f1 = 25 Hz

25

50

75

Frequency

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Modal Parameter Estimation – Stabilization Diagram ▪ Compare modal parameters at current order with previous order ▪ Increase the model order until modes stabilize

n : new pole : frequency : damping : all

Model Order

o f d s

Amplitude

Stability

0 Frequency

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DEMONSTRATION: MDOF Curve Fitting on Flat Plate

Mode Indicator Function 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

Double “dip” indicates two modes at same frequency

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Why are rigid body modes seen at high frequencies?

Modal Assurance Criterion 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%)

1 .5 0

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MAC Example

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MAC = 100% correlation Siemens PLM Software

MAC Example

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MAC = 0.015 (1.5% correlation) Siemens PLM Software

MAC Example

6 Points

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764 Hz and 385 Hz - MAC = 0.96 (96% correlation) Siemens PLM Software

MAC Example

15 Points

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764 Hz and 385 Hz - MAC = 0.03 (3% correlation) Siemens PLM Software

MAC for flat plate with 6 DOFs

1

.5

0

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Spatial Aliasing – not enough response points Siemens PLM Software

DEMONSTRATION: SDOF Peak Picking on Plate (15points)

MAC for flat plate with 15 DOFs

1

.5

0

No High Off Diagonal Correlations Unrestricted © Siemens AG 2019 Page 120

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Polymax MDOF Curve Fitting

LSCE versus LMS PolyMAX LSCE

LMS PolyMAX

-For smaller models

+Large number of responses

-High computational load

+Fast, efficient computation

-High damping is a problem

+High damping no problem

-High modal density

+High modal density

-Not for broadband analysis

+Broadband analysis

-Unclear stabilization diagram

+Crystal-clear stabilization diagram

Not all MDOF curve fitters are created equal ! Unrestricted © Siemens AG 2019 Page 122

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Modal Parameter Estimation - LSCE

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Modal Parameter Estimation – LMS Test.Lab PolyMax

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DEMONSTRATION: PolyMAX Modal Analysis

PolyMAX Validation Studies

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 – Comparing Mode Shapes

MAC matrix

▪ MAC matrix

LSCE (X) – FE (Y)

▪ PolyMAX (X) – FE (Y)

PolyMAX yields good correlation to higher frequency Unrestricted © Siemens AG 2019 Page 129

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PolyMax Validation – “Noisy” FRFs 1.00

/ Amplitude

(

Log

(m/s2)/N

)

1.00

10.0e-6 4.00

Hz Linear

20.00

180.00 4.00

Linear

20.00

F F

° Phase

Hz

Coherence w ing:vvd:+Z/Multiple Coherence back:vde:+Y/Multiple

0.05

-180.00 Hz

Multiple Coherence

Hz

FRFs

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PolyMax Validation – “Noisy” FRFs

LSCE Unrestricted © Siemens AG 2019 Page 131

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PolyMax Validation – “Noisy” FRFs

LMS PolyMAX Unrestricted © Siemens AG 2019 Page 132

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PolyMax Validation – FRF Synthesis with PolyMax

g/N

( ) Log

10.0e-3

( ) Log

g/N

0.10

100e-6 4.00

Hz Linear

20.00

1.00e-6 4.00

Hz Linear

20.00

180.00 4.00

Linear

20.00

180.00 4.00

Linear

20.00

Hz

° Phase

° Phase

Hz

-180.00

-180.00 Hz

Left wing

Hz

Back of the plane

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PolyMax Validation – Lightly Damped Structures

Stabilization

FRF synthesis

) Log (

(m/s2)/N

1.00

10.0e-6 10.00 180.00 10.00

Hz Linear

64.00

Linear

64.00

° Phase

Hz

-180.00 10.00

Hz

64.00

PolyMAX alleviates the need to use a different curve fitter algorithm for heavy and lightly damped structures Unrestricted © Siemens AG 2019 Page 134

Siemens PLM Software

Advanced Techniques

#1 – Automatic Mode Expansion

Test Mesh

STL File Unrestricted © Siemens AG 2019 Page 136

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DEMONSTRATION: Modal Expansion

Multi-Run Modal: Transmission

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Multi-Run Modal: Transmission

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Siemens PLM Software

Multi-Run Modal: Transmission

MOVE 1

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Multi-Run Modal: Transmission

MOVE 1

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Siemens PLM Software

Multi-Run Modal: Transmission

MOVE 1 MOVE 2

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Siemens PLM Software

Multi-Run Modal: Transmission

MOVE 1 MOVE 2

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Siemens PLM Software

Multi-Run Modal: Transmission

MOVE 1 MOVE 2

MOVE 3

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Siemens PLM Software

Multi-Run Modal: Transmission

MOVE 1 MOVE 2

MOVE 3

Are the frequencies of the structure the same between Move 1, Move 2 and Move 3? Unrestricted © Siemens AG 2019 Page 145

Siemens PLM Software

Multi-Run Modal: Transmission

Could one versus all accelerometers make a difference?

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Multi-Run Modal: Transmission

Which one of these mode shapes is more likely to be affected by accelerometer mass loading? Unrestricted © Siemens AG 2019 Page 147

Siemens PLM Software

Multi-Run Modal: Transmission

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Siemens PLM Software

Multi-Run Modal: Transmission

Does placing at top versus bottom have different frequency shift effect? Unrestricted © Siemens AG 2019 Page 149

Siemens PLM Software

MOVE 3 A/F

MOVE 2 A/F

MOVE 1 A/F

Multi-Run Modal: Transmission

Hz

Hz

Which Frequency is right? Unrestricted © Siemens AG 2019 Page 150

Siemens PLM Software

Multi-Run Modal: Transmission 1.18

1.00

Amplitude

g/N Amplitude

MOVE 1

Unrestricted © Siemens AG 2019 Page 151

Sum FRF SUM 0.01 404.43 404.43

Siemens PLM Software

Hz

915.01 0.00 915.01

Multi-Run Modal: Transmission

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Siemens PLM Software

Multi-Run Modal: Transmission 1.00

ALL MOVES

EVEN THIS ONE IS EFFECTED

Amplitude

g/N Amplitude

0.89

Unrestricted © Siemens AG 2019 Page 153

Sum FRF SUM 0.01 404.43 404.43

Siemens PLM Software

Hz

915.01 0.00 915.01

Multi-Run Modal: Transmission – All Data Sets

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Siemens PLM Software

Multi-Run Modal: Transmission – Single Data Set

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Siemens PLM Software

MOVE 1 A/F

Multi-Run Modal: Transmission

MOVE 2 A/F

Partial Shape 1

MOVE 3 A/F

Partial Shape 2

Partial Shape 3

Hz

Hz

Complete Shape Unrestricted © Siemens AG 2019 Page 156

Siemens PLM Software

Multi-Run Modal: Transmission

ANALYZE ALL MOVES AT ONCE

ANALYZE EACH MOVE SEPARATELY AND COMBINE (MULTI-RUN)

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DEMONSTRATION: Multi Run Modal

Correlation

“Old” Product Design Cycle Product Design Process

TIME

Functional Activities Unrestricted © Siemens AG 2019 Page 161

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“Modern” Product Design Process Product Design Process ▪ Simulate product performance before prototypes are available

TIME ▪ Use single prototype & testing for validation

Functional Activities Unrestricted © Siemens AG 2019 Page 162

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Pretest & Correlation: Process Improvement

Product 1

Product 2

TIME

TIME

Correlation

Correlation

Pretest

Pretest

Analysis

Analysis FE Modeling

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Process Improvement Siemens PLM Software

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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Modal Assurance Criterion ▪ Modal Assurance Criterion (MAC) describes how similar the shapes are for a given mode pair using a scale of 0 to 1

1 .5 0

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MAC Example

MAC = 100% Unrestricted © Siemens AG 2019 Page 166

Siemens PLM Software

MAC Example

MAC = 1.5% Unrestricted © Siemens AG 2019 Page 167

Siemens PLM Software

MAC Example

6 Points

764 Hz and 385 Hz - MAC = 96% Unrestricted © Siemens AG 2019 Page 168

Siemens PLM Software

MAC Example

15 Points

764 Hz and 385 Hz - MAC = 3% Unrestricted © Siemens AG 2019 Page 169

Siemens PLM Software

Application Case: Exhaust System

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Siemens PLM Software

Exhaust Mode at 15 Hz

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Exhaust Mode at 15 Hz

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Siemens PLM Software

Exhaust Modes at 15 and 130 Hz

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Exhaust Modes at 15 and 130 Hz

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Siemens PLM Software

6 Exhaust Modes up to 137 Hz

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Siemens PLM Software

FEA Model Pretest, Correlation, Updating Tools Simcenter Testlab

Simcenter3D

•

•

• • •

View and Animate Modes from Simulation (Nastran, Abaqus, Ansys, etc) and Test View and overlay FRFs (Nastran) from Simulation and Test Modal Data Acquisition (Shakers, Impact) Mode Shape Correlation (MAC)

•

• • • •

View and Animate Modes from Simulation (Nastran, Abaqus, Ansys, etc) and Test (Universal file and Testlab) View and overlay FRFs (Nastran) from Simulation and Test (Universal File) Pretest Analysis Mode Shape Correlation (MAC) MAC Contribution Updating via Solution 200 in Nastran

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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 •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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Siemens PLM Software

Application Case: Pretest Analysis Step 3: Use 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 offdiagonal MAC of <0.15

Additional Accel’s

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Application Case: Pretest Analysis Step 3: Use 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 offdiagonal terms.

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Siemens PLM Software

Simcenter3D Pretest and Correlation

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Application Case: Pretest Analysis Step 5: Create wireframe geometry for Modal Test and export to Simcenter Testlab software. • A Testlab 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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Siemens PLM Software

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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Siemens PLM Software

Application Case: Correlation Step 1: Use the 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

Unrestricted © Siemens AG 2019 Page 184

Siemens PLM Software

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

Unrestricted © Siemens AG 2019 Page 185

Siemens PLM Software

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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Siemens PLM Software

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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Siemens PLM Software

MAC Contribution 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

Unrestricted © Siemens AG 2019 Page 188

Siemens PLM Software

MAC Contribution

TEST

FE

Unrestricted © Siemens AG 2019 Page 189

Siemens PLM Software

MAC Contribution

TEST

FE

Unrestricted © Siemens AG 2019 Page 190

Siemens PLM Software

MAC Contribution

TEST

FE

Unrestricted © Siemens AG 2019 Page 191

Siemens PLM Software

MAC Contribution

MAC WILL NOT CHANGE MUCH

TEST

FE

Unrestricted © Siemens AG 2019 Page 192

Siemens PLM Software

MAC Contribution

MAC WILL CHANGE A LOT

TEST

FE

Unrestricted © Siemens AG 2019 Page 193

Siemens PLM Software

Application Case: Sensitivity & Updating Step 4: Sensitivity Analysis and FE Model Updating Sensitivity Analysis: •Consideration of physical exhaust system leads engineer to consider effect of weld on this junction (ignored in the FE model) FE Model Updating: • Manual updating • Element thickness increased locally in weld location • Amount of thickness increase guided by MAC and Frequency correlation

Unrestricted © Siemens AG 2019 Page 194

Siemens PLM Software

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 •Sensitivity Analysis & Nastran SOL200 FE Model updating

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Siemens PLM Software

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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Siemens PLM Software

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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Siemens PLM Software

Pretest & Correlation: Conclusion 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

Simcenter3D 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

Unrestricted © Siemens AG 2019 Page 198

Siemens PLM Software

QUIZ

What can an FRF tell you? 16.0

(m/s2)/N Amplitude

Resonant Frequency

Damping

14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 0.0 10.00

Hz Linear

950.00

180 10.00

Linear

950.00

Mode Shape ➢ Requires Multiple FRFs

° Phase

Hz

-180 10

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

950

Hz Unrestricted © Siemens AG 2019 Page 200

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What is this? 10.4

g/lbf Amplitude

ss ss ss ss ss ss ss ss ss ss ss ss ss ss ss ss ss df sd dd df f df f o

sv sv sd sv sv sf os s fs s s s s s s s s s s s s s s s o f o

s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s v v ov o v v s o o

s s s s s s s s s s s s s s s s s s s s s s v o

o

s s s s s s s s s s s s s s s s s s s s s s s d f s o

s s s s s s s s s s s s s s s s s s s s s s o

s s f s d v f s s s f s s s v s d s v s df f s ss o s s s s s f s ss s dv s df s ss s sv s f o s d s s d d f v d d f f f s f o o o o

o o

d d d d d o

o o

32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5

63.3e-3 85.1

Linear Hz

837

Unrestricted © Siemens AG 2019 Page 201

Siemens PLM Software

What is MAC abbreviation for?

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Siemens PLM Software

What is MAC abbreviation for?

Modal Assurance Criterion

Unrestricted © Siemens AG 2019 Page 203

Siemens PLM Software

What is MAC abbreviation for?

Modal Assurance Criterion

Unrestricted © Siemens AG 2019 Page 204

Siemens PLM Software

IS THIS A “GOOD” MAC?

205 copyright LMS International - 2005

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Siemens PLM Software