Crested Waves in Thermoelastic Plates Immersed in Liquid

Abstract

The propagation of circularly crested generalized thermoelastic waves in a homogeneous 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 conventional coupled thermoelasticity, and Lord-Shulman and Green-Lindsay theories of thermoelasticity. We derive secular equations for a circular homogeneous isotropic plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms. Results for the uncoupled theory of thermoelasticity have been obtained as a particular case from the present one. Special cases, such as Lam6 modes, short wavelength waves, and thin plate waves of the secular equation, are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for aluminum epoxy composite material bordered with water. The dispersion curves for symmetric and antisymmetric wave modes and amplitudes of displacement and temperature change in the case of fundamental symmetric (SO) and skew symmetric (AO) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.