Surface waves in a pre-stressed elastic body

Abstract

The bearing of the Barnett–Lothe formulation of the theory of elastic surface waves in a crystalline medium on surface motions of a pre-stressed elastic body is examined in this paper. The main results are a general uniqueness theorem and the notion of a neutral set, bounding the domain of existence of surface waves and interpretable as the totality of standing wave solutions. As an application of these ideas a full account is given of the existence of surface waves in a homogeneously deformed elastic body possessing a restricted form of the Hadamard strain-energy function. In conclusion, the difficulties involved in treating an analysis of surface waves as a test of the stability of a loaded semi-infinite elastic body are briefly discussed.