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 [Formula: see text] wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium [Formula: see text] having an incident wave and a thermoelastic diffusion medium [Formula: see text] 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 [Formula: see text] a quasi-mass diffusion wave [Formula: see text], a quasi-thermal wave [Formula: see text] and one is a transverse wave [Formula: see text]. 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.