Investigation of the scattering of Lamb waves from a generalized circular cavity by using Poisson/Mindlin plate theories and numerical simulation

Abstract

A mathematical model for the scattering of a symmetric $S_0$ Lamb wave mode from a circular cavity in an isotropic plate is developed that can handle both symmetric and asymmetric single- and double-sided blind holes. The theoretical formulation is based on Mindlin and Poisson plate theories. A finite element model is also utilized to extract the scattering patterns of Lamb waves from various cases of a generalized circular cavity. Two-dimensional FFT analysis is used to determine the transmitted and reflected Lamb wave modes when the incident wave interacts with either symmetric (through-hole and double-sided blind hole) or asymmetric (blind hole and double-sided blind hole) cavities. Results indicate that the remaining thickness of a cavity zone and the type of a cavity are two key parameters in the scattering pattern. For asymmetric cavities, the shape of the scattering pattern of the mode-converted $A_0$ mode does not vary significantly. However, the amplitude of the scattering pattern shows noticeable changes in the out-of-plane component of the displacement. Results obtained from the proposed theory and finite element model are in good agreement with previously published data.