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Research Papers

Modeling Guided Waves for Damage Identification in Isotropic and Orthotropic Plates Using a Local Interaction Simulation Approach

[+] Author and Article Information
Shankar Sundararaman

Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907-2031

Douglas E. Adams1

Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907-2031deadams@purdue.edu

1

Corresponding author.

J. Vib. Acoust 130(4), 041009 (Jul 11, 2008) (16 pages) doi:10.1115/1.2890389 History: Received April 19, 2007; Revised October 20, 2007; Published July 11, 2008

In this paper, a numerical simulation technique based on the local interaction simulation approach (LISA)/sharp interface model (SIM) is used to study the propagation of Lamb waves in aluminum and orthotropic plates and wave interactions with damage. The LISA/SIM model allows for accurate and fast simulations of sharp changes in material properties across interfaces associated with damage or specimen boundaries. Damage in the form of holes and changes in density and/or stiffnesses are studied for three different plates. These local changes in density and stiffness have dimensions not exceeding the wave length of the interrogating wave form. Wave scatter from these damage sites is shown at different time instants and at specific spatial locations. Multiple site damage cases are studied for all the plate structures. The different scatter patterns associated with intersecting and nonintersecting surface cracks are also studied. Results obtained from a combination of single site damage cases are compared with the composite multiple site damage case to study the usability of commonly applied algorithms for identifying damage. The benefits of observing multiple directions of the displacement field are demonstrated. It is shown that the out-of-plane measurements give a clearer indication of damage sites than the in-plane measurements.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Rayleigh–Lamb dispersion relations for a 2mm aluminum plate with elastic modulus 70GPa and Poisson’s ratio of 0.334 (a) phase velocity and (b) wave number dispersion curves

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Figure 2

Input forcing function: five wave Hanning window modulated tone burst

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Figure 3

Schematic showing typical plate model with actuator

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Figure 4

Spatial out-of-plane displacement (w displacement) responses at time instances ((a), (d), and (g) 37.5μs, (b), (e), and (h)) 62.5μs, and (c), (f), (i) 150μs and at a frequency of 80kHz in a 300×300×2mm3 aluminum plate. (a)–(c) are from the pristine plate, (d)–(f) are from the damaged plate, and (g)–(i) are the differences between the damaged plate response and the pristine plate response.

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Figure 5

Peak amplitude of the difference time data between pristine and damaged data for (a) increasing damage intensity as illustrated in the accompanying table (b) and (c) changing stiffness and density as illustrated in the table (d). The sensor location is at (5,245,0)mm in a 300×300×2mm3 aluminum plate with actuator placed at (5,295,0)mm. The stiffnesses and densities are expressed in (b) and (d) as percentage changes in relation to the rest of the plate.

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Figure 6

Spatial out-of-plane displacement (w-displacement) responses at time instances (a) 37.5μs, (b) 62.5μs, and (c) 150μs denoting the difference responses at a frequency of 80kHz in a 300×300×2mm3 aluminum plate

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Figure 7

Spatial out-of-plane displacement (w-displacement) responses at time instance ((a) and (d)) 37.5μs and ((b) and (e)) 62.5μs, and ((c) and (f)) 150μs and at a frequency of 80kHz in a 300×300×2mm3 aluminum plate. (a)–(c) are from the pristine plate, and (d)–(f) are the difference between the damaged plate response and the pristine plate response. Actuator located at (5,295,0)mm.

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Figure 8

Spatial out-of-plane displacement (w-displacement) responses at 200μs with an actuator located at ((a) and (c)) (150,5,0)mm and ((b) and (d)) (5,295,0)mm at a frequency of 80kHz in a 300×300×2mm aluminum plate. (a) and (b) are from the pristine plate, and (c) and (d) are the differences between the damaged plate response and the pristine plate response.

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Figure 9

(a) Comparison of difference time data for three instances of damage sites at three locations on the plate structure illustrating the different times of arrival and amplitudes at the sensor location. (b) Comparison of difference data between a plate structure with the three damage locations and the sum of the comparisons illustrated in Fig. 9. The sensor location is at (5,245,0)mm in a 300×300×2mm3 aluminum plate with actuator placed at (5,295,0)mm.

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Figure 10

Spatial in-plane displacement responses (v-displacement) with displacements directed parallel to the width dimension at time instances (a) and (d) 37.5μs, (b) and (e) 62.5μs, and (c) and (f) 150μs and at a frequency of 80kHz in a 300×300×2mm aluminum plate. (a)–(c) are from the pristine plate, and (d)–(f) are the difference between the damaged plate response and the pristine plate response. Actuator located at (5,295,0)mm.

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Figure 11

Stacked absolute of the difference spatial response at time instants between 1.25μs and 500μs in an aluminum plate structure with multiple instances of damage. (a) and (d) are the u displacements, (b) and (e) are the v displacements, and (c) and (f) are the w displacements. (d)–(f) are the zoomed versions of the damage located at (280,157,0.25)mm.

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Figure 12

Stacked absolute of the damaged plate spatial response at time instants between 1.25μs and 500μs in an aluminum plate structure with damage in the form of a through hole of different sizes. In all cases, the w-displacement result is shown.

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Figure 13

Stacked absolute of the damaged plate spatial response at time instants between 1.25μs and 500μs in an aluminum plate structure with a through hole of different sizes. (a) and (d) are the u displacements, (b) and (e) are the v displacements, and (c) and (f) are the w displacements. The surface slices are obtained at the center of the plate.

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Figure 14

Spatial out-of-plane (z-direction) difference spatial responses at time instances ((a), (d), and (g)) 37.5μs (b), (e), and (h) 62.5μs, and (c) (f) and (i) 150μs and at a frequency of 80kHz in a 300×300×2mm3 aluminum plate with surface damage in the form of ((a)–(c)) nonintersecting damage, ((d)–(f)) completely intersecting damage, and ((g)–(i)) partially intersecting damage.

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Figure 15

Stacked absolute of the difference spatial response at time instants between 1.25μs and 500μs in an aluminum plate structure with surface damage in the form of (a) nonintersecting damage, (b) completely intersecting damage, and (c) partially intersecting damage. (a) is the u displacement, (b), (d), and (e) are the v displacements, and (c) is the w displacement.

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Figure 16

Stacked absolute of the damaged plate spatial response at time instants between 1.25μs and 500μs in an aluminum plate structure with through the thickness damage in the form of (a) nonintersecting damage, (b) completely intersecting damage, and (c) partially intersecting damage. (a), (d), and (g) are the u displacements, (b), (e), and (h) are the v displacements, and (c), (d), and (f) are the w displacements.

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Figure 17

450×250×3mm3 orthotropic plate specimen showing the displacement profiles of a pristine specimen subject to an excitation at 160kHz corresponding to an actuator at ((a)–(c)) (5,125,0)mm and ((d)–(f)) (225,245,0)mm. Responses are obtained for all three displacements, i.e., (a) and (d) are the u displacements, (b) and (e) are the v displacements, and (c) and (f) are the w displacements.

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Figure 18

450×250×3mm orthotropic plate specimen showing the displacement profiles of the difference between a damaged specimen and a pristine specimen subject to an excitation at 160kHz corresponding to an actuator at ((a)–(c)) (5,125,0)mm and ((d)–(f)) (225,245,0)mm. Responses are obtained for all three displacements, i.e., (a) and (d) are the u displacements, (b) and (e) are the v displacements, and (c) and (f) are the w displacements.

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