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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Outline
• Introduction• Concept• Numerical examples• Experimental results• Conclusions and future work
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Concept• 1D waveguide:
1D stress in x<x0 region:
where
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Concept• 1D waveguide:
Letting:Harmonic wave
gives:
2D FFT:
Incident
Reflected
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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)
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Concept• 2D example: plane and spherical wave at frequency ωo
Plane wave Spherical wave3D FFT:
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
−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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Concept• 2D example: two spherical waves at frequency ωo
3D FFT:
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
−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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Numerical results: 1D rodResponse at x=3/4 L 2D FFT
Filtered Response at x=3/4 L Filtered 2D FFT
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Experimental result 1
• Al Plate with 4 slits of controlled dimensions
4
3
2
1
Actuator
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Measured response Filtered response
90 kHz excitation
Experimental results: plate with 4 cracks
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
RMS of the filtered response:
Experimental results: plate with 4 cracks
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
−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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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).
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
Experimental results: honeycomb plate
Measured response RMS of filtered response
Area of damage
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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.
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
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
Massimo RuzzeneSchool of Aerospace [email protected]: (404) 894 3078
THANK YOUAcknowledgements:
Mr. V. Sharma of Millennium Dynamics Co.Dr. J. Smith of Corning Co.