Special inhomogeneous plane waves in cubic elastic materials

Abstract.

The purpose of this paper is to present new special explicit inhomogeneous plane wave solutions of the linearized equations of motion for elastic cubic crystals. It is based upon the “directional-ellipse” method which leads to an eigenvalue problem for the complex symmetric acoustical tensor. The solutions are obtained by considering a special case for which the determination of the three complex eigenvalues of this tensor reduces to finding the three complex cubic roots of a real positive number. Explicit simple expressions are presented for the slowness and amplitude bivectors.