Thermomechanical Interactions in a Rotating Non-Local Functionally Gradient Orthotropic Elastic Half-Space Along-with Three Phase Lag and Hyperbolic Two-Temperature

The present paper aims to study the reflection phenomena of plane waves in a rotating, non-local, functionally graded orthotropic thermoelastic half-space with a three-phase lag. Normal mode analysis is used to obtain the solution and the boundary is assumed to be stress-free having the influence of the impedance parameter. The analytical solution to the problem reveals the existence of a quasi longitudinal wave (QL), quasi transversal wave (QT), and a quasi thermal wave (T). Amplitude ratios are derived corresponding to the incidence of each wave. With the help of these amplitude ratios, energy ratios are obtained and presented graphically demonstrating the impact of the functionally graded parameter (FG) and various heat conduction models. The energy ratios depend on the angle of incidence as well as the properties of the medium. The nature of dependence is distinct for distinct reflected waves. The obtained results justify that the summation of energy ratios is unity at each angle of incidence, which thus proves the law of conservation of energy. Moreover, comparative analysis has also been performed with dual phase lag model (DPL) and Lord Shulman model (LS). The results obtained through the investigation are useful to study the rock structure and thermoelastic properties of the inner structure of the earth.