Interaction effects from the elastodynamic scattering by two symmetric spherical cavities

Abstract

The scattering of harmonic waves has been studied extensively for problems in quantum mechanics, acoustics, electromagnetics, and elasticity. Solutions to elastodynamic problems are the basis for ultrasonic non-destructive evaluation measurement models. Therefore, in this study, we investigate the use of the boundary element method (BEM) in the frequency domain using an off-boundary technique in which the observation points are taken inside the scattering object. This methodology removes both non-integrable singularities from the domain of integration along with avoiding ill-conditioning effects that occur at fictitious eigenfrequencies of which both require using special computationally demanding procedures to obtain solutions. Additionally, we employ both free and half-space fundamental solutions (Green’s displacement tensors) to investigate the elastodynamic scattering of an incident, plane, time-harmonic longitudinal wave in the frequency domain of a homogeneous, isotropic, and linear elastic solid with one or two spherical cavities. The half-space fundamental solution reduces the number of required boundary elements in half, which significantly reduces computational resource requirements. We only consider spherical cavities in this paper to illustrate the full and half-space off-boundary BEM and analyze the interaction effects associated with the elastodynamic scattering by two symmetric spherical cavities. To verify the validity of the free and half-space off-boundary BEM formulations, surface displacement results are compared with existing surface displacement results and show good agreement. Finally, the half-space off-boundary BEM is used to illustrate the interaction effects of the back and forward scattered displacement fields as a function of the distance from the spherical cavities.