Plane harmonic waves for three thermoelastic theories

Plane harmonic thermoelastic waves predicted by two theories, which incorporate second sound effects, are investigated. An isotropic solid is assumed and the theories are linear, consequently the strain is infinitesimal and temperature changes are small compared with the reference temperature. Results from the two theories, for material properties representative of aluminum, are compared with those obtained from the classical theory that has been treated in detail by Chadwick One purpose of the paper is to investigate the validity of one of the second sound theories, which is based on the Principle of Local State and the Maxwell-Cattaneo relation. This theory violates a consequence of the Clausius-Duhem relation but it is shown that, for the relaxation time considered, this violation is negligible for plane harmonic waves, except for frequencies of order of magnitude of 10 GHz or greater. The relationship between characteristic theory and the theory of plane harmonic waves, for the thermoelastic wave problem, discussed.