Initial Stress and Gravity on P‐Wave Reflection from Electromagneto‐Thermo‐Microstretch Medium in the Context of Three‐Phase Lag Model

Abstract

The present paper studied the reflection of thermo-microstretch waves under the generalized thermoelasticity theory which is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the electromagnetic field, initial stress, and gravity. The formulation is applied under the thermoelasticity theory with three-phase lag, and the reflection coefficient ratio variations with the angle of incidence under different conditions are obtained. Numerical results obtained from the present study are presented graphically and discussed. It is observed that the initial stress, gravitation, and electromagnetic field exert some influence in the thermo-microstretch medium due to reflection of P-waves.

Response of impedance parameters on waves in the micropolar thermoelastic medium under modified Green‐Lindsay theory

“…For a harmonic plane wave propagation in the direction, where the wave normal vector lies in x 1 ‐x 3 plane making an angle θ 0 with the positive x 3 ‐axis normal to the surface, the solution of Equations ()–() may be assumed as Bayones et al. [21], $$\begin{equation} \left( {{\rm{q}},{\rm{\ T}},{\rm{\ \psi }},\ {\phi }_2} \right) = \left( {{{\rm{q}}}^{\rm{o}},{\rm{\ T}}^{\rm{o}},{\rm{\ \psi }}^{\rm{o}},\ {\phi }_2^{\rm{o}}} \right)\ {{\rm{e}}}^{{\rm{\iota \kappa }}({{\rm{x}}}_1\sin {{{\theta}}}_0 - {{\rm{x}}}_3\cos {{{\theta}}}_0 + {\rm{\nu t}})}, \end{equation}$$where ι is known as iota, κ denoted as wave number and quantities such as $${{\rm{q}}}^{\rm{o}},{\rm{\ T}}^{\rm{o}},{\rm{\ \psi }}^{\rm{o}},\ {\phi }_2^{\rm{o}}$$ are arbitrary constants.…”

“…For a harmonic plane wave propagation in the direction, where the wave normal vector lies in x 1 -x 3 plane making an angle 𝜃 0 with the positive x 3 -axis normal to the surface, the solution of Equations ( 13)-( 16) may be assumed as Bayones et al [21],…”

The gravitational field effect on a micro-elongated thermoelastic layer under a fluid load with two theories

“…Later, based on the model of DPL modification of Fourier’s law, a series of articles was considered by Othman and Abd-Elaziz (2020), Abo-Dahab et al. (2020), Bayones et al. (2021b, c, 2022), Elhag et al.…”

“…Roy-Choudhuri (2007) noted DPL model effects in elastic layer half-space for single-dimensional thermoelastic waves. Later, based on the model of DPL modification of Fourier's law, a series of articles was considered by Othman and Abd-Elaziz (2020), Abo-Dahab et al (2020), Bayones et al (2021bBayones et al ( , c, 2022, Elhag et al (2022).…”

An analytical method for the spherical stress wave equation in linear hardening materials

“…Many researchers also have studied the analytical solutions of the elastic-plastic spherical stress wave equation [4][5][6][7][8][9][10][11], but the effects of the unloading on the stress wave propagating has not been considered yet in the existing analytical solutions. In recent years, much attention has been paid to the influence of thermal field, electromagnetic field, rotation, initial stress and gravitation on the stress wave propagation and reflection [12][13][14][15][16][17][18]. However, researchers pay less attention to the influence of plasticity.…”