Analytic Solution for the Secular Equation of Gravity and Magnetic Field Variation on Propagation of Surface Waves in Fibre-Reinforced Anisotropic Thermoelastic Solid with Hydrostatic Initial Stress and Two Relaxation Times

The aim of this paper is to investigate the analytic solution for the secular equation of surface waves in fibre-reinforced anisotropic solid thermoelastic of a two-dimensional problem under the variation of the gravity, thermal relaxation times, hydrostatic initial stress and magnetic field. The generalized theory of surface waves developed and then it has been employed to investigate particular cases of waves, viz., Rayleigh, Stoneley and Love waves. The wave velocity equations have been illustrated for different cases and are in well agreement with the corresponding classical result, when the effect of gravity, magnetic field, relaxation times and parameters for fibre-reinforced of the material medium are neglected. Finally, the influence of gravity, magnetic field, hydrostatic initial stress and relaxation times on the secular equation are computed numerically as a complex; its real part is the surface wave velocity and the imaginary part is the attenuation coefficient and then displayed graphically.