FLEXURAL AND EXTENSIONAL WAVES PROPAGATION IN TRANSVERSELY ISOTROPIC PLATES IN GENERALIZED THERMOELASTICITY

摘要

In this paper, the boundary value problem concerning the propagation of plane harmonic thermoelastic waves in flat infinite homogeneous transversely isotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations for a heat conducting thermoelastic plate corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. The horizontally polarized SH wave gets decoupled from the rest of motion and propagates without dispersion or damping, and is not affected by thermal variations on the same plate. A numerical solution to the frequency equations for an aluminum plate (isotropic) and zinc plate (transversely isotropic) is given, and the dispersion curves 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 phase velocity of the waves is 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.