GL Model on Reflection of P and SV Waves from the Free Surface of Thermoelastic Diffusion Solid Under Influence of the Electromagnetic Field and Initial Stress |
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| Authors: | M N M Allam S Z Rida S M Abo-Dahab R A Mohamed |
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| Affiliation: | 1. Mathematics Department, Faculty of Science , Mansoura University , Mansoura , Egypt;2. Mathematics Department, Faculty of Science , South Valley University , Qena , Egypt;3. Mathematics Department, Faculty of Science , South Valley University , Qena , Egypt;4. Mathematics Department, Faculty of Science , Taif University , Taif , Saudi Arabia |
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| Abstract: | This article is devoted to estimating the influence of magnetic field, electric field and initial stress in an elastic solid half-space under thermoelastic diffusion. The governing equations in the xz-plane are solved taking into consideration the Green–Lindsay (GL) model. The Reflection of dilatational (P) wave and Shear Vertical (SV) wave split into four waves: namely, P wave, thermal wave, mass diffusion wave and SV wave. The reflection phenomena of P and SV waves from the free surface of an elastic solid with thermoelastic diffusion under influence of magnetic field, electric field and initial stress is considered. The expressions for the reflection coefficients for the four reflected waves are obtained. These reflection coefficients are found to depend upon the angle of incidence θ of P and SV waves, thermoelastic diffusion, magnetic field, electric field and initial stress and other material parameters. The numerical values for the reflection coefficients are calculated analytically and presented graphically for varying values of these parameters. |
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| Keywords: | Electric field GL-Model Initial stress Magnetic field Mass diffusion P and SV waves Reflection coefficients Thermoelasticity |
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