Abstract
In generalized thermoelasticity Fourier's law of heat conduction in the classical theory of thermoelasticity is modified by introducing a relaxation time associated with the heat flux. Equations are derived for the squared wave speeds of plane harmonic body waves propagating through anisotropic generalized thermoelastic materials subject to thermomechanical constraints of an arbitrary nature connecting deformation with either temperature or entropy. In contrast to the classical case, it is found that all wave speeds remain finite for large frequencies. As in the classical case, it is found that with temperature-defonnation constraints one unstable and three stable waves propagate in any direction but with deformation-entropy constraints there are three stable waves and no unstable ones. Many special cases are discussed including purely thermal and purely mechanical constraints.