Problem of p- and SV-waves reflection and transmission during two media under three thermoelastic theories and electromagnetic field with and without gravity

In this paper, we investigated the primary wave (p-wave) and shear (SV-wave) reflection and refraction during solid-liquid media under three thermoelastic theories and electromagnetic field with and without initial stress and gravity. We will deal the problem of reflection and refraction of thermoelastic waves at interface between two different media in the presence of initial stress and magnetic field in the context of three thermoelastic theories: CT (Classical theory), GL (Green-Lindsay) and DPL (Dual-Phase-Lag). Boundary conditions at the interface between the two media concern: (i) continuity of the displacement, (ii) neglecting the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) neglecting the tangential stress and continuity of the temperature have been considered. The reflection and refraction coefficients for the incident p- and SV-waves have been obtained as functions of angle of incidence, initial stress, electromagnetic field, and gravity. Special cases for presence or absence of gravity or initial stress are investigated. The magnitudes of reflection and refraction coefficients ratios for the incident waves have been computed numerically and displayed in graphs to show the physical meaning of the phenomenon.

Automated summary

This paper investigates the reflection and refraction of primary and shear waves in solid-liquid media under three thermoelastic theories, including initial stress and gravity. The study focuses on the behavior of thermoelastic waves at interfaces between different media with initial stress and magnetic fields, considering various thermoelastic theories. Results show the reflection and refraction coefficients as functions of angle of incidence, initial stress, electromagnetic field, and gravity, with special cases of presence or absence of initial stress or gravity being examined. Numerical calculations of reflection and refraction coefficients ratios for incident waves are presented to illustrate the phenomenon.