Explicit conditions for the existence of exceptional body waves and subsonic surface waves in anisotropic elastic solids

Abstract

It is known that a subsonic surface (Rayleigh) wave exists in an anisotropic elastic half-space x 2 ⩾ 0 if the first transonic state is not of Type 1. If the first transonic state is of Type 1 but the limiting wave is not exceptional, a subsonic surface wave exists. If the first transonic state is of Type 1 and the limiting wave is exceptional, a subsonic surface wave exists when tr L ( υ ˆ ) ⩽ 0 . It is shown that an exceptional body wave is necessarily an exceptional transonic wave, and could be an exceptional limiting wave. Only two wave speeds are possible for an exceptional body wave. We present explicit conditions in terms of the reduced elastic compliances s α β ′ for the existence of an exceptional body wave. If an exceptional body wave exists, conditions are given for identifying whether the transonic state is of Type 1. Hence, through the existence of an exceptional body wave we provide explicit conditions for the existence of a subsonic surface wave with the exception when tr L ( υ ˆ ) needs to be computed.