The behaviour of elastic surface waves polarized in a plane of material symmetry I. General analysis

Abstract

In all reported instances of surface-wave transmission in anisotropic elastic media in which the speed of propagation is supersonic in relation to the slowest branch of homogeneous plane waves, the reference plane of the surface wave is a plane of material symmetry of the medium and the displacement is polarized in this plane. It is proved herein that whenever the symmetry group of the transmitting material admits a plane of reflexional symmetry ∏ a surface wave having ∏ as its reference plane excites no displacement orthogonal to ∏ and, subject to specified conditions, may travel with a speed in the supersonic range. A general existence-uniqueness theorem for such waves is established and the determination of the displacement field and the traction on planes parallel to the boundary is shown to require only the evaluation of four definite integrals, the location of the real zero of a combination of these integrals and the solution of a quartic equation. The analysis developed in part I is applied in parts II and III to media with monoclinic, orthorhombic and cubic symmetries.