Abstract
The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of Rayleigh wave at the canyon-shaped flaws on the surface, both in forward and inverse aspects. Firstly, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns into the traditional BEM equation set. Results show that the modified BEM is an efficient and accurate approach for calculating far-field reflection coefficients. Secondly, we propose an inverse reconstruction procedure for the flaw shape using reflection coefficients of Rayleigh wave. By theoretical deduction, it can be proved that the objective function of flaw depth d(x1) is approximately expressed as an inverse Fourier transform of reflection coefficients in wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and good agreements are shown between the reconstructed flaw images and the geometric characteristics of the actual flaws.
Highlights
The non-destructive testing and structural health monitoring are of great importance in civil, mechanical, and aerospace engineering industries
One of pioneering work can be attributed to Ayster and Auld’s paper of calculating the scattered field of Rayleigh waves by surface crack [3], which is followed by Achenbach, who discussed the emission of surface waves from a crack by cyclic loading in detail [4]
To verify the modified boundary element method (BEM) method, we try to solve the classical Rayleigh wave scattering problem presented by Kawase [10], for which the solutions have already been obtained from discrete wavenumber method applying half-space Green functions
Summary
The non-destructive testing and structural health monitoring are of great importance in civil, mechanical, and aerospace engineering industries. Of reflected wave with surface-breaking cracks [20,21,22,23] or notches [24,25], both in experimental and numerical aspects, in order to achieve flaw location and sizing effect These researchers mainly adopted pitch-catch configurations, and were able to detect the positions and approximate sizes of defects, but lacked further information, such as depth, width, and severity. Boundary integral equation over the flaw area, it can be proved that the objective function of flaw depth d(x1 ) is approximately expressed as an inverse spatial Fourier transform of reflection coefficients in wavenumber domain This inversion procedure is especially suitable for reconstruction of weak and shallow notches, and can be used as an initial-step image for deeper and steeper canyons.
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