BASIC PROPERTIES OF PLANE HARMONIC WAVES IN A PRESTRESSED HEAT-CONDUCTING ELASTIC MATERIAL

This paper is concerned with the propagation of plane harmonic waves of small amplitude in a heat-conducting elastic body of unrestricted symmetry that is not stress free in its undisturbed state. The novelty of the treatment given here consists first in a derivation of the secular equation in a form that makes transparent the association of low- and high-frequency behavior with isentropic and isothermal conditions, and second in the introduction of a multivalent modal function whose regular branches determine the complex slownesses of the possible modes of wave propagation in a given direction. The development of a general analysis of harmonic waves on this basis yields a natural classification of the modes and leads, via a standard result in the theory of algebraic functions, to series representations of modal properties that are valid near the extremes of the frequency range. Attention is subsequently directed to situations in which simplified features of the kind displayed by thermoelastic waves in an initially stress-free isotropic medium are realized. This part of the work is prompted by ideas first evolved in connection with singular surfaces, and the paper concludes with an appraisal of the relationships between harmonic and acceleration waves in the context of thermoelasticity.