Plane harmonic waves in strongly elliptic thermoelastic materials with microtemperatures

This paper is concerned with the linear theory of thermoelasticity with microtemperatures, which permits the transmission of heat as thermal waves of finite speed, following the theory of Green and Naghdi. We study the propagation of plane harmonic waves in an unbounded strongly elliptic thermoelastic material with microtemperatures. We are able to prove that there is no dispersion and only undamped waves are possible. In the isotropic case we give the explicit analytic expression for the phase velocity of the waves. In particular we find that all transverse waves happen at constant temperature.