Rectilinear oscillations of a rigid inclusion in an infinite elastic medium

Abstract

In this paper we present an exact analysis of the problem of rectilinear oscillations of a rigid inclusion in the shape of a convex body of revolution. The method is one of boundary-perturbation technique. For convenience, we have confined our attention to the case of axisymmetry, although the method can be used fruitfully for other nonaxisymmetric problems. In the way of illustration, we have applied the technique to the cases of a perturbed sphere and an oblate spheroid. In the latter case we have calculated the force necessary to maintain steady oscillations of the spheroid correct to first order in frequency.