Point singularities and the singularity method in classical elastodynamics

Abstract

The object of the article is to elucidate the application of the singularity method in classical elastodynamics. To this end, solutions for higher–order point singularities, e.g. time–harmonic concentrated moment, centre of dilatation, centre of rotation and force tensor, are derived from the influence tensor by a method usually employed in the theory of electrostatics for the study of potential of a system of charged particles. Solutions of some elastodynamic problems concerning spherical cavities and rigid spherical inclusions are then derived by combining these point singularities.