Abstract
This thesis considers two related problems concerning rigid inclusions embedded in elastic media. The first problem considered is the determination of the first two terms, in the expansion for low frequencies, of the scattering cross-section for both P- and S- waves incident upon a rigid inclusion of arbitrary shape. The particular case of an ellipsoid is discussed in detail and specific results are obtained for the special cases of a prolate spheroid, a sphere, an elliptic disc and a circular disc. In the second part of the thesis, approximate expressions are obtained for the force on an arbitrary rigid inclusion embedded in an elastic space when the inclusion is subjected to a given displacement. The solutions are obtained as perturbations of the solutions for the inclusion in an infinite medium and the first order correction for small values of the ratio (fundamental dimension of inclusion / minimum distance from the boundary) is obtained. Elastic spaces in the form of plates, half-spaces and infinitely long cylinders are considered, with various boundary conditions being prescribed. Inclusions of elliptic and other related shapes are considered. In both problems integral equation methods are used, the problems and their solutions being discussed in more detail in the respective introductions.