Frequency-Wavenumber Domain Filtering For Damage...

Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078

Frequency-Wavenumber Domain Filtering For Damage Visualization

Massimo RuzzeneSchool of Aerospace EngineeringGeorgia Institute of Technology

Atlanta, GA

August 3, 2006

QNDE 2006Review of Progress in Quantitative Nondestructive Evaluation

Portland, OR July 31-August 4, 2006


Outline

• Introduction• Concept• Numerical examples• Experimental results• Conclusions and future work


Introduction

• Work investigates the application of guided waves (Lamb) for SHM;

• Lamb waves are detected through a Scanning Laser Doppler Vibrometer (SLDV);

• SLDV allows the detection and the visualization of the full wavefield as it propagates in the structure.

• Resulting images describe the main features of the propagating wave and show its interactions with discontinuities along the wave path

• Damage can be thus immediately detected and localized through limited processing.


Introduction

• In addition, wavefield time-domain data allow the application of Multi-dimensional Fourier Transforms (2D/3D FFTs):

– Representation of the response in the frequency/wavenumber domain.

• 2D/3D FFTs allow:

– The analysis of multi-mode wave signals and the characterization of the various modes;

– The identification of dispersion relations;– Highlighting all wave components propagating in directions opposite

to the direction of the main injected pulse;– The detection of presence of reflections and mode conversions

caused by damage.


Introduction

Objective:

• Application of the frequency/wavenumber representation to devise simple filtering strategies for:

– Eliminating the applied excitation and corresponding propagating wave from the recorded response, while

– Highlighting the presence of any reflections along the wave path.


Concept• 1D waveguide:

1D stress in x<x0 region:

where


Concept• 1D waveguide:

Letting:Harmonic wave

gives:

2D FFT:

Incident

Reflected


ConceptIncident

Reflected

0

5

10

15

20

−20

−10

0

10

200

0.2

0.4

0.6

0.8

1

ω [rad/s]kx [rad/m]

Incident

Reflected


Conceptk x [

rad

/m]

ω [rad/s]0 2 4 6 8 10 12 14 16

−15

−10

−5

0

5

10

15

Incident

Reflected

Filtered response

Original response

k x [ra

d/m

]

ω [rad/s]0 2 4 6 8 10 12 14 16

−15

−10

−5

0

5

10

15

= window function(2D Hanning)


Concept• 2D example: plane and spherical wave at frequency ωo

Plane wave Spherical wave3D FFT:


−300 −200 −100 0 100 200 300

−200

−150

−100

−50

0

50

100

150

200

kx [rad/m]

k y [ra

d/m

]

3D FFT @ ω=ω0

−300 −200 −100 0 100 200 300

−200

−150

−100

−50

0

50

100

150

200

kx [rad/m]

k y [ra

d/m

]

Filtered 3D FFT @ ω=ω0

Snapshot of original waveform

Snapshot of filtered waveform


Concept• 2D example: two spherical waves at frequency ωo

3D FFT:


−300 −200 −100 0 100 200 300

−200

−150

−100

−50

0

50

100

150

200

kx [rad/m]

k y [ra

d/m

]

−300 −200 −100 0 100 200 300

−200

−150

−100

−50

0

50

100

150

200

kx [rad/m]

k y [ra

d/m

]

3D FFT @ ω=ω0

Filtered 3D FFT @ ω=ω0

Snapshot of original waveform

Snapshot of filtered waveform


Numerical results• 1D damaged rod:

– Rod is modeled using FE method (160 bar elements);– Excitation is a 5-cycles 50 kHz sinusoidal burst;– Damage is modeled as a thickness reduction at

selected location.


Numerical results: 1D rodResponse at x=3/4 L 2D FFT

Filtered Response at x=3/4 L Filtered 2D FFT


Numerical results• 2D elastic domains with longitudinal cracks:

– Wave propagation is simulated according to the Mass Spring Lattice Model (MSLM);

– Domains have dimensions Lx=0.5 m and Ly=0.25 m, and they are discretized using a 200*100 lattice;

– Excitation is a 5-cycles 100 kHz sinusoidal burst;– Damage is modeled as a 30% stiffness reduction.


Numerical results: 2D elastic domainOne crack

k y [ra

d/m

]

kx [rad/m]

−250 −200 −150 −100 −50 0 50 100 150 200 250

−150

−100

−50

0

50

100

150

k y [ra

d/m

]

kx [rad/m]

−250 −200 −150 −100 −50 0 50 100 150 200

−150

−100

−50

0

50

100

150

3D FFT @ f=100 kHz

Filtered 3D FFT @ f=100 kHz

Original response

Filtered response


k y [ra

d/m

]

kx [rad/m]

−250 −200 −150 −100 −50 0 50 100 150 200 250

−150

−100

−50

0

50

100

150

k y [ra

d/m

]

kx [rad/m]

−250 −200 −150 −100 −50 0 50 100 150 200 250

−150

−100

−50

0

50

100

150

Numerical results: 2D elastic domainTwo cracks

3D FFT @ f=100 kHz

Filtered 3D FFT @ f=100 kHz

Original response

Filtered response


Experimental results

Function generator 1

Function generator 2

DAQ &

Signal processing

Trigger

Plate

Low-frequencysignal (1 Hz)

Phase information

Reconstructedwave-form

Plateresponse

Sinusoidalburst

(1) (2)

(4) (3)

LDV Head

Voltage Amplifier

Measured Wave-field

Set-up for wave-field detection/visualization


Experimental result 1

• Al Plate with 4 slits of controlled dimensions

4

3

2

1

Actuator


Experimental results: plate with 4 cracksExample of 3D FFT of recorded response

kx [rad/m]

ky [

rad

/m]

−200 −150 −100 −50 0 50 100 150 200−200

−150

−100

−50

0

50

100

150

200

kx [rad/m]

ky [

rad

/m]

−200 −150 −100 −50 0 50 100 150 200−200

−150

−100

−50

0

50

100

150

200

Cross section at excitation frequency (90 kHz)

Original response Filtered response


Measured response Filtered response

90 kHz excitation

Experimental results: plate with 4 cracks


RMS of the filtered response:

Experimental results: plate with 4 cracks


Experimental result 2

• Tongue and groove connection

• Epoxy is used for bonding;• Bonding defect is simulated by preventing epoxy to reach middle

part of the connection.


Experimental results: Tongue and groove

Tongue and Grove Joint

Damage Location

PiezoceramicActuator Disc

Tongue and Grove Joint

Damage Location

PiezoceramicActuator Disc

Measured responseSet up and area of scanning


−0.04 −0.02 0 0.02 0.04 0.06 0.08

−0.04

−0.02

0

0.02

0.04

0.06

y [m

]

x [m]

Disbond length

RMS of the filtered response:

Experimental results: Tongue and groove


Experimental result 3• Honeycomb plate

• Face sheets are bonded to the core with epoxy;• Grease is placed over a small area to prevent bonding (defect simulation).


Experimental results: honeycomb plate

Measured response RMS of filtered response

Area of damage


Conclusions• Simple filtering technique based on spectral

representation of a wavefield;

• Technique is demonstrated on analytical and numerical results;

• Experimental application is enabled by the use of a Scanning Laser Vibrometer;

• Results are presented for various types of damage;– Localized and distributed;– Single plate, built-up structure and honeycomb.

• Technique is model independent.


Future work

• Application to composites;

• Formulate a damage index that quantifies the level of damage based on the amplitude of the filtered scattered signal;

• Utilize the filtered signals as baseline data for comparison with a damaged configuration.

• Refine the filtering strategy to eliminate reflections from known structural features.


Future workF-15 Wing Panel:• Presence of stiffeners complicates the wavefield;• Waves are reflected and tend to propagate perpendicularly to stiffeners

Snapshot of panel response at 30 kHz

Actuator location


THANK YOUAcknowledgements:

Mr. V. Sharma of Millennium Dynamics Co.Dr. J. Smith of Corning Co.

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Frequency-Wavenumber Domain Filtering For Damage...

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