Interaction of a plane compressional elastic wave with a rigid spheroidal inclusion

Abstract

In this paper we have considered the problem of diffraction of a plane compressional harmonic elastic wave by a rigid spheroidal inclusion embedded in a homogeneous isotropic medium. For simplicity we have confined our attention to the axisymmetric case when the incident wave propagates along the axis of symmetry of the spheroid. The inclusion is assumed to be movable. Since the exact solution to this problem is not obtainable analytically we have used a boundary perturbation technique that is applicable at any finite frequency. We have derived exact analytical expression for the amplitude of oscillation of the inclusion correct to first order in a shape correction factor ϵ \epsilon . It is shown that the low-frequency expansion of the amplitude agrees with the expansion derived by other means correct to first order in frequency. We have also given a high-frequency expansion of the amplitude. Furthermore, we have derived the asymptotic expansion of the field in the illuminated zone and have shown that these are compatible with those obtained by an application of Keller’s ray theory.