Mode-exciting method for Lamb wave-scattering analysis

Abstract

This paper presents an innovative method, called the mode-exciting method, to solve Lamb wave-scattering problems in an infinite plate. In this method, a set of Lamb wave modes is excited by appropriate boundary conditions given on the virtual edges of a finite plate. After solving numerically the elastodynamic problem defined in the finite domain, the numerical solution is decomposed into Lamb wave modes. The Lamb wave modes constitute a system of equations, which can be used to determine the scattering coefficients of Lamb waves for the original problem in an infinite plate. The advantage of the mode-exciting method is that a well-developed numerical method such as finite-element (FEM) or boundary element (BEM) can be used in the elastodynamic analysis for the finite region without any modification like coupling with other numerical techniques. In numerical examples, first the error estimation of the mode-exciting method is discussed by considering three types of error indicators. It is shown that among them, the power ratio of nonpropagating modes to propagating modes is the most suitable for the error estimation. Numerical results are then shown for scattering coefficients as a function of nondimensional frequency for edge reflection and crack scattering problems.

Reflection of Obliquely Incident Guided Waves by an Edge of a Plate

“…Similarly to the derivation shown in our previous paper, 12) it can be shown that P mn has the physical meaning as follows:…”

“…Note that since the reflection problem is a symmetric problem in the thickness direction, the symmetric and antisymmetric modes are uncoupled each other. For comparison, the results obtained by the mode-exciting method 12) are also shown by symbols. Very good agreement is found between both results.…”

“…12) In particular case that ¼ 0, we have m ¼ k m and the orthogonality shown in eq. (15) reduces into the orthogonality shown in our previous paper.…”

“…(15) reduces into the orthogonality shown in our previous paper. 12) If m ¼ Ã n , the direct substitution of eqs. (10) and (13) into eq.…”

Shape Reconstruction of Plate Thinning Using Reflection Coefficients of Ultrasonic Lamb Waves: a Numerical Approach

“…A similar approach using SH guided waves has been proposed by Wang and Hirose. 13) In the formulation of the inverse method, the far field expressions of the Green's function for a plate waveguide are firstly deduced, and are then substituted into the integral expression of scattered waves by flaws subjected to a single incident Lamb mode. Furthermore, introducing Born approximation into the integral formula yields the Fourier transform pair between a thinning-flaw shape, which is expressed by the depth as a function of the longitudinal coordinate, and reflection coefficients in frequency domain.…”