Nonclassical dynamical thermoelasticity

Abstract This paper describes the modern approaches to the analytical treatment of dynamical thermoelasticity. It has been a well known fact that the classical heat conduction equation does not describe the phenomenon of heat propagation correctly. Contrary to the solutions of the classical heat conduction equation, which predicts the infinite speed of the heat wave, the experimental results indicate that heat travels with finite speed. The same results apply to thermoelastic waves. Therefore, the modern approaches to this problem depend on appropriate modifications of the classical heat conduction equation. Five such approaches are described in the paper: (a) Lord and Shulman (L–S) theory; (b) Green and Lindsay (G–L) theory; (c) Hetnarski and Ignaczak (H–I) theory; (d) Green and Naghdi (G–N) theory; and (e) Chandrasekharaiah and Tzou (C–T) theory. Some evaluation and comparison of the results that follow from these five descriptions is provided.

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