Waves propagation for magneto-thermoelastic medium during the two-temperature theory with the gravitational field

Abstract

The interaction between the generalized thermoelasticity theory and two-temperature theory is studied in the context of the two-dimensional (2D) deformation processes of an elastic medium. The influences of the gravitational field, hydrostatic initial stress, and magnetic field are used during the problem discretion in the context of the Lord-Şhulman (L-S) theory, the Green-Naghdi theory of type III (G-N III), and the three-phase-lag model (3PHL). The general solutions are obtained when the interaction between different fields (gravity field and magnetic field) occurs. The harmonic vibration technique in the physical domain is used to obtain the main exact expressions (physical quantities) for the waves’ velocity and attenuation coefficients for (i) Stoneley waves, (ii) Love waves, and (iii) Rayleigh waves. Different types of boundary conditions, according to the heating processes, are taken into account. Comparisons are carried out according to the effect of relaxation times (three theories of thermoelasticity). The obtained results are calculated numerically and presented graphically with some comparisons in the absence and the presence of the gravity field, the hydrostatic initial stress, and the magnetic field.