Conditions admitting the existence of type 3 transonic states in stable anisotropic linear elastic media

Abstract

Central to the theory of subsonic free surface waves in anisotropic linear elastic half-spaces is the notion of the first transonic state, of which there are six ordinary types and four extraordinary types. The type 3 ordinary transonic state corresponds to a slowness section in which all three slowness branches make tangential contact at a single point; hence, this transonic state is an example of an acoustic axis of triple degeneracy. In this work we examine the possible existence of type 3 states in media of isotropic, hexagonal, trigonal, tetragonal and cubic symmetry. Only stable media of hexagonal and tetragonal symmetry admit type 3 states, and our analysis fully delineates the orientations and restrictions on the elastic stiffnesses associated with the existence of these states.