Foundations of the Theory of Surface Waves in Anisotropic Elastic Materials

Abstract

This chapter discusses that rapid progress has been made in recent years in the investigation of the basic aspects of the theory of surface waves in anisotropic elastic media. Solutions have been found to the fundamental problems concerning the existence and uniqueness of free surface waves, and in this respect, it can be claimed that a complete theory is now in existence. The outstanding new ideas have of late come from a rather unexpected quarter—namely, the theory of dislocations and results of major significance may consequently lie hidden from specialists in the dynamics of elastic materials who do not habitually attend to developments in this field. The chapter highlights that the possibility of oversight is not reduced by the dependence of the main contributions on a multitude of sources mostly located in the literature of solid-state physics, much of the precursory material having no obvious connection with elastic surface waves. Two broad insights into the character of elastic surface waves confirmed by the present study are that a free surface wave is intrinsically a subsonic phenomenon and that the set of directions on a particular anisotropic elastic half-space in which such waves can travel is determined by the slowness surface of the material.