DEGENERACIES IN THE THEORY OF PLANE HARMONIC WAVE-PROPAGATION IN ANISOTROPIC HEAT-CONDUCTING ELASTIC MEDIA

This paper explores the unusual hierarchy of degeneracies in the linea r theory of thermoelasticity. In classical elastic wave theory all deg eneracies take the form of acoustic axes! that is directions in which two or all three plane bulk waves have equal speeds. In dynamical ther moelasticity four plane harmonic waves can travel in an arbitrary dire ction, and there are two types of degeneracy. The first type arises wh en two or more waves have equal slownesses, normally complex, and the second type when the coefficient matrix of the governing system of dif ferential equations has a repeated zero eigenvalue. Each type of degen eracy is of two possible kinds, so the number of cases in which at lea st one degeneracy occurs is eight. It is shown that only three of thes e possibilities can actually exist and in only one of them are both ty pes of degeneracy present. The effects of thermomechanical interaction on the modes of wave propagation are then minimal. An analysis of the degeneracies, their interconnexion and their influence on the nature of thermoelastic waves occupies the first part of the paper. In the se cond part the relationship of classical elastodynamics to linear therm oelasticity is studied, in respect of degeneracy, by considering small thermoelastic perturbations of an acoustic axis. The underlying degen eracy is either removed by the perturbation or divided into one or two pairs of thermoelastic degeneracies. The directions in which the new degeneracies appear are determined and the properties of the associate d degenerate waves discussed in detail.