Generalized thermoelastic waves in anisotropic plates sandwiched between liquid layers

The propagation of waves in a homogeneous, transversely isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides, is investigated in the context of Lord–Shulman (LS), Green–Lindsay [GL] and Green–Nagdhi (GN) theories of thermoelasticity. Secular equations for homogeneous, transversely isotropic plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for isotropic materials, coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion of wave propagation and occurs along an in-plane axis of symmetry. The special cases, such as short wavelength waves, thin plate waves and leaky Lamb waves of the secular equations are also discussed. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for transversely isotropic plate of zinc material bordered with water. The dispersion curves for symmetric and antisymmetric wave modes, attenuation coefficient and amplitudes of displacement and temperature change in case of fundamental symmetric (S0) and skew symmetric (A0) modes along the direction making an angle of 45° with the axis of symmetry are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.