Acceleration waves and ellipticity in thermoelastic micropolar media

Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel-Hadamard-Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave's propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented.