Behavior of Energy Ratios Under Higher-order Mdd at Distinct Media

Abstract

This paper presents a novel mathematical model of orthotropic piezothermoelastic half-space under the reference of three-phase lags heat transfer law with higher-order memory-dependent derivatives (HPS) underlying a thermoelastic half-space (TS). Thermoelastic plane waves involving longitudinal P wave, thermal T wave, or transversal SV wave propagating via TS medium and hitting at the interface x3 =0 results in three waves reflected in the TS medium and four waves transmitted in the HPS medium. Amplitude ratios are determined at the boundary interface x3 =0 and used to obtain the energy ratios of various reflected and transmitted waves. It is noticed that these ratios are under the impact of phase lags, higher order MDD parameters, frequency of the waves, and other physical parameters involved in the model. The balance law of energy conservation is justified. Graphically illustrated the impact of higher order memory-dependent derivatives parameters on the energy ratios variation with the incidence angle. Some unique cases of interest are also deduced