Boundary-polarized subsonic Rayleigh waves under conditions of semi-simple Stroh degeneracy

Abstract

We undertake a study of subsonic free surface (Rayleigh) waves in linear elastic half-spaces of general anisotropy when the wave polarization vector lies in the half-space boundary , if and when the formalism due to A. N. Stroh exhibits semi-simple degeneracy at the Rayleigh speed v R . It is shown that the class of subsonic steady wave motions at any subsonic velocity exhibiting semi-simple degeneracy includes a free surface wave whenever the first transonic state is not exceptional, in accordance with general surface wave theory. Furthermore, such a free surface wave is always necessarily boundary-polarized ! In general, the restrictions on the half-space elastic constants permitting the existence of semi-simplicity in steady motion at a subsonic phase speed are not satisfied in any physically realized medium which is elastically stable, but we outline an algorithm which allows one to construct the elastic stiffnesses of media which exist mathematically and allow for the existence of subsonic free surface waves (which are necessarily boundary-polarized) under conditions of semi-simple degeneracy in the sense of Stroh's formalism.