Structure and intrinsic properties of dispersion relation in hyperbolic thermoelasticity

For a system of field equations of hyperbolic thermoelasticity, we derive a propagation condition for a thermoelastic disturbance in a form of homogeneous plane wave in deformation and temperature. The corresponding dispersion relation is given in an explicit form, together with the dependence of characteristic coefficients on the principal invariants of the tensor of isothermal elasticity, heat conductivity, and thermoelasticity. Discussion of different types of homogeneous thermoelastic plane waves is given as well. Derived methodology is applied in the analysis of Green–Naghdi model.