Waves in thermoelastic solid half‐space containing voids with liquid loadings

Abstract

AbstractThe influence of the voids in the propagation of time‐harmonic plane waves in a semi‐infinite homogeneous isotropic thermoelastic medium in contact with inviscid liquid half‐space has been explored under the Lord‐Shulman theory of thermoelasticity. The incompressible and non‐viscous liquid is taken in the upper half‐space and the effect of gravity on the whole system is assumed to be negligible. The mathematical model is developed and the exact expressions for the considered variables are obtained by using the normal mode analysis method. The compact secular equation for the considered model is derived for thermally insulated and isothermal cases respectively. There exist four waves in the generalized thermoelastic porous solid half‐space and one wave exists in the liquid half‐space. In the solid half‐space, one is a transverse wave and the remaining three is the set of coupled dilatational waves. The coupling among these waves is because of the presence of voids and thermal effects, also the amplitude of oscillation of these waves decreases with time. The transverse wave in the solid half‐space is undamped in time and remains independent of the effects of voids and heat. The particle's motion is deduced for Rayleigh wave propagation and found to be elliptical in solid half‐space and circular in liquid half‐space. Also, the plane of particle motion is tilted due to the presence of void parameters in the medium. Magnesium crystal has been chosen for the numerical computation and the discussion of various graphs depicting the profiles are presented in the last section.