Extensional thermoelastic waves in transversely isotropic plate according to a higher order theory

The objective of this work is to provide a rigorous analysis of thermoelastic ultrasonic waves in transversely isotropic plates. Characteristic features such as dispersion curves of thermoelastic waves of plates are investigated and the influence of coupling in the heat equation on these features is critically examined. If the propagation of the waves is along the axis of symmetry of the plate, then it is possible to decouple the antisymmetric modes from the symmetric ones. This is conveniently done in approximate theories by retaining and omitting various terms in the expansions for the displacement and temperature. In this work, it is assumed that the wave propagation is along the axis of symmetry of an infinite anisotropic plate. Hence, extensional (symmetric) modes can be investigated apart from the antisymmetric modes. Displacement and temperature are expanded across the thickness of the plate using Legendre polynomials. Obviously, such a theory best fits those applications where a low frequency pulse is employed. Further, keeping only the leading terms in the expansion of displacement and temperature gives rise to a lower order theory, which predicts well the correct behavior of symmetric modes in relatively smaller frequency range. Results also show that the effect of coupling in the heat equation is insignificant for thermoelastic waves and can be ignored.