Analysis of the steady oscillations of a plane absolutely rigid inclusion in a three-dimensional elastic body by the boundary element method

Abstract

The three-dimensional problem of the involvement of a plane absolutely rigid inclusion of specified mass in the field of a harmonic wave propagating in an infinite elastic body is considered by means of integral equations with a singularity of the Helmholtz potential. A boundary-element algorithm is proposed for constructing a discrete analogue of the equations, taking into account the fact that the solutions belong to a class of functions which increase on the contour of the integration region (the region of the defect). The dependence of the displacements of the inclusions as a rigid whole and also the stress concentration in its neighbourhood on the wave number is investigated for two cases of the diffraction by a disc-shaped inclusion of a plane longitudinal wave with a wave front that is parallel and perpendicular to it.