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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.

The present paper concerned with the reflection and transmission of plane wave from a plane surface separating a micropolar viscoelastic solid (MVES) half-space and a fluid-saturated (FS) incompressible porous solid half-space is studied. A longitudinal wave ($P$-wave) or transverse wave (SV-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained with the help of boundary conditions at the interface. Then, these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with the angle of incidence of the incident wave. It is found that these amplitude ratios depend on the angle of incidence of the incident wave as well as on the properties of media. From the present investigation, a special case, when FS porous half-space reduces to empty porous solid and MVES half-space reduces to micropolar elastic solid, has also been deduced and discussed with the help of graphs.

The problems of elastic wave propagation in the micropolar porous materials have been attempted under the interaction of micro-rotation tensor and porous distribution in this material. We obtain the existence of three coupled longitudinal and two coupled shear waves propagating with different phase speeds. Numerically, the phase speed and attenuation of five basic waves are computed. We consider the incident plane waves at the boundary of micropolar porous materials, then the dispersive nature of the incident waves is studied and the existence of critical angle for the incident shear wave is found. The amplitude and energy ratios of various reflected waves for the incident coupled longitudinal and shear waves are obtained analytically and numerically. Further, the influence of different material parameters is studied using dispersion relation and the relevant numerical values.