Stress and Flux Free Thermoelastic Vibrations in Plates of Anisotropic Media with Two Thermal Relaxation Times

Abstract

Analysis for the propagation of waves in homogenous heat conducting infinite monoclinic stress and flux free thermoelastic plate of finite thickness is developed. Frequency equations in closed form and isolate the mathematical conditions for symmetric (extensional) and antisymmetric (flexural) thermoelastic wave mode propagation in completely separate terms are derived. Higher symmetry material, such as orthotropic, transversely isotropic, cubic and isotropic is contained implicitly in the analysis. It is shown that the motion for SH modes decouple which is not effected by thermal variations from the rest of motion if propagation occurs along an in-plane axis of symmetry. Finally the Numerical solution of the frequency equations for zinc plate is carried out, and the dispersion curves for the first six modes are presented. The three motions namely, longitudinal, transverse and thermal of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The dispersion curves are get modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.