Surface Waves, Limiting Waves and Exceptional Waves: David Barnett's Role in the Development of the Theory

Abstract

A short review is presented of progress in the theory of localized eigenwaves in anisotropic solids. The main attention is paid to the problem of existence of surface wave solutions in semi-infinite elastic bodies. Here the contribution of David Barnett is most important. The general theorems of existence and uniqueness are formulated and their modifications for media with piezoelectric and/or piezomagnetic couplings are considered. The conditions for existence of supersonic surface waves in purely elastic half-spaces are displayed. The situations on both sides of the vicinity of exceptional transonic states are discussed. The criterion for the existence of quasi-bulk subsonic surface waves in elastic media of unrestricted anisotropy is obtained in terms of the general Barnett and Lothe theorem. The conditions for the existence of exceptional bulk waves and their main properties are considered. The interface wave theory of David Barnett et al is reviewed for rigid and slip contacts between elastic and piezoelectric sub-media.