Dual‐phase‐lag model on magneto‐thermoelastic rotating medium with voids and diffusion under the effect of initial stress and gravity

Abstract

In this paper, the propagation of harmonic plane waves is considered in a generalized thermoelastic medium with diffusion and voids in the presence of initial stress, magnetic field, rotation, and gravity in the context of thermoelastic models; classical, Lord Shulman, Green Lindsay as well as dual-phase-lag models. We applied the boundary conditions in the physical domain using the normal mode method technique on the surface to obtain the displacements, stresses, temperature, diffusion concentration, and the volume fraction field. Influence of initial stress, magnetic field, rotation, and gravity on temperature, stresses, concentration of diffusion, and the volume fraction is observed through a numerical example.The results obtained will be compared in the presence and absence of the new considered variables, also with the previous results obtained by the others and displayed graphically.diffusion, dual-phase-lag, electromagnetic, gravity, Green-Lindsay, initial stress, Lord-Shulman, normal mode analysis, rotation, voids | INTRODUCTIONAny study on the propagation waves in generalized thermoelasticity materials can be significant in structural engineering, geophysics, and seismology. Such a study becomes more realistic if the presence of initial stress, magnetic field, rotation, and gravity could be considered. Lord and Shulman 1 introduced the generalized theory of thermoelasticity with one relaxation time considering an isotropic body. The linear theory of elastic materials under the influence of voids in investigated by Cowin and Nunziato. 2 Aouadi 3 presented a generalized thermoelastic diffusion problem based on the theory of Lord and Shulman with one relaxation time in anisotropic media. Aouadi 4 proved the generalized thermoelastic diffusion problem, based on the theory of Lord and Shulman using Laplace transforms technique for a uniqueness theorem for these equations. A generalized thermoelastic one-dimensional (1D) diffusion in infinite medium with a spherical cavity subjected to a time-dependent thermal shock of its internal boundary which is assumed to be traction free is pointed out by Aouadi. 5 Singh 6,7 investigated the reflection of P and SV waves from the generalized thermodiffusion free surface of an elastic solid. Nowacki 8-10 illustrated dynamical problems of thermoelastic diffusion in solids. Olesiak and Pyryev 11 discussed the influence of the cross effects arising from the coupling of the fields of mass diffusion, temperature, and strain in an elastic cylinder. Sherief and Saleh 12 discussed the generalized thermoelastic theory with diffusion in half-space solid. Ram et al 13 studied the thermomechanical response of generalized thermoelastic diffusion with one relaxation time because of the time-harmonic sources. Effect of viscosity and diffusion on generalized magnetothermoelastic interactions on a spherical cavity isotropic body is discussed by Bayones. 14 Abo-Dahab and Singh 15 illustrated the influence of the magnetic field in an elastic solid half-space under thermoelastic diffusion. Xi...

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