Effect of three-phase-lag thermal and three-phase-lag diffusion models on waves at the boundary of elastic and thermoelastic diffusion medium

Abstract

In this paper, we discuss the reflection and refraction of an incident P wave or $SV$ wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium $M_1$ having an incident wave and a thermoelastic diffusion medium $M_2$ with TPLT (i.e., three-phase-lag thermal) and TPLD (i.e., three-phase-lag diffusion) models. It has been noticed that two waves are reflected and four are refracted in an isotropic thermoelastic diffusion medium. Out of the four refracted waves, three are longitudinal waves: a quasi-longitudinal wave $qP,$ a quasi-mass diffusion wave $qV$, a quasi-thermal wave $qT$ and one is a transverse wave $SV$. If we consider the above waves first, the amplitude and energy ratio are calculated by using the surface boundary conditions and then graphically represented to compare the change in energy and amplitude ratio with the change in incident angle for three particular cases. The conservation of energy is depicted by verifying that all the energy sums up to unity. The considered problem has its application in earthquake engineering, astronautics, rocket engineering, seismology and many more engineering areas.