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

Abstract

This paper presents an inverse method for the shape reconstruction of local surface-thinning flaws on a 2-D isotropic plate using ultrasonic guided Lamb waves. The problem considered is to determine the function representing a plate thinning shape from reflection coefficients of Lamb waves obtained over a range of frequency, when a single Lamb wave mode is incident upon the thinning part in a plate. The formulation is based on the integral expression of scattered waves by flaws in a plate. Introducing the far field approximation and Born approximation into the integral expression, we obtain the Fourier transform pair between the shape function of plate thinning and reflection coefficients in frequency domain. Thus the shape of a plate-thinning flaw can be reconstructed by performing the inverse Fourier transform of reflection coefficients of Lamb waves with respect to frequency. Some numerical examples are illustrated to show the validity and effectiveness of the inverse approach. Reflection coefficients of the first symmetric Lamb wave mode are calculated by a forward analysis, and are used for the inverse analysis. It is found that although the reconstructed flaw shapes do not perfectly agree with the original shapes due to the approximations induced in the inverse approach, the flaw location and depth are well estimated if the frequency range for the inverse Fourier transform is chosen properly, corresponding to the flaw configurations.