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Research Papers

Accuracy and Convergence Using a Local Interaction Simulation Approach in One, Two, and Three Dimensions

[+] 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. Appl. Mech 76(3), 031008 (Mar 09, 2009) (10 pages) doi:10.1115/1.2871105 History: Received April 19, 2007; Revised October 20, 2007; Published March 09, 2009

Guided waves are utilized in structural health monitoring for identifying damage in material components. Simulations can be used to examine how elastic waves propagate in components to help in selecting measurement and data analysis techniques. In this work, the influence of grid size and the frequency sample rate on the amplitude accuracy and convergence of local interaction simulation approach/sharp interface model (LISA/SIM) numerical simulations are studied as they pertain to guided wave propagation in structural materials. These issues are studied in all three dimensions, and amplitude distortion with respect to the Courant–Friedrich–Lewy criterion is explored. The LISA/SIM enables accurate and fast modeling of localized and sharp changes in material properties across interfaces associated with heterogeneities and/ or boundaries. The validity of the simulation is demonstrated by comparing simulated responses with experimentally measured data. Additionally, Lamb wave dispersion curves are extracted through the course of the convergence study using a broadband pulse and the two-dimensional fast Fourier transform method.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Rayleigh–Lamb wave-number-frequency dispersion relations for (a) 2mm and (b) 6.6mm aluminum plates with an elastic modulus of 70GPa, density of 2700kg∕m3, and Poisson’s ratio of 0.334

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Figure 2

Simulation results input signal: (a) tone burst and (b) sinc pulse (with dashed line indicating typical start of signal used in the simulation)

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Figure 3

Schematic setup showing typical plate model with actuator for the (a) one-, (b) two-, and (c) three-dimensional models

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Figure 4

Amplitude variation as a function of sampling frequency and spatial sampling for the one-dimensional model

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Figure 5

Amplitude variation as a function of sampling frequency and spatial sampling for a three-dimensional plate model

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Figure 6

Convergence plot for varying grid sizes for a plate of dimensions 600×2mm2; center frequency of input signal: 20kHz; sensor location (0,100)mm

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Figure 7

Convergence plot for varying grid sizes for a plate of dimensions 600×4mm2; center frequency of input signal: 20kHz; sensor location (0,100)mm

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Figure 8

Convergence plot for varying grid sizes for a plate of dimensions 150×2mm2; center frequency of input signal: 20kHz; sensor location (0,100)mm

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Figure 9

Convergence plot for varying grid sizes for a plate of dimensions 600×2mm2; center frequency of input signal: 20kHz; sensor location (0,0)mm, actuator location (0,300)mm

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Figure 10

Dispersion curve simulation results for a 609.6×609.6×2mm3 aluminum plate with a grid spacing of 1mm in all three dimensions extracted from excitation using (a) a rectangular pulse and (b) a half-sinc pulse

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Figure 11

Dispersion curve simulation results for a 609.6×2mm2 aluminum section with a grid spacing of 1×1mm2. Boxed region indicates typical region in which experimental analysis is carried out using Lamb waves by health monitoring researchers.

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Figure 12

Dispersion curve simulation results for a 609.6×2mm2 aluminum section with a grid spacing of 1∕8×1∕8mm2

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Figure 13

Dispersion curve simulation results for a 609.6×2mm2 aluminum section with a grid spacing of 1∕16×1∕16mm2

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Figure 14

Comparison of experimental and numerical results obtained at two grid dimensions for a 609×609×2mm3 aluminum plate

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Figure 15

Comparison of experimental and numerical results obtained for a 1×1×1mm3 grid and a 1×1×0.25mm3 grid for a 300×300×2mm3 plate at 20kHz

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