Properties of type 6 transonic states with respect to grazing incidence reflection of bulk waves at planar free or clamped surfaces of half infinite elastically anisotropic media

Abstract

Recognizing different characteristics of reflection of P, SV and SH waves at the planar surface of a half infinite isotropic elastic medium, the properties of Type 6 transonic states with respect to grazing incidence reflection of bulk waves are investigated by generalization of the case of grazing incidence reflection at Type 1 transonic states. It is shown that for grazing incidence reflection related to Type 6 transonic states, which are always composite exceptional, the reflection can have two different features, skimming reflection or repellent reflection. For a free surface, the reflection is skimming or repellant according to whether the incident wave is associated with an exceptional or composite exceptional limiting wave or a non-exceptional wave, respectively. It is also proven that the self-orthogonality of limiting waves and the completeness of the Stroh eigenvector system for Type 6 transonic states reveal a series of linear dependence/independence relations between the Stroh eigenvector components. These relations are significant for establishing a theoretical framework for the description of two component surface waves and spaces of simple reflection.