The Effect of Dual-Phase-Lag Model on Reflection of Thermoelastic Waves in a Solid Half Space with Variable Material Properties

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity: Lord-Shulman (L-S) theory with one relaxation time, Green-Naghdi (G-N) theory without energy dissipation and Tzou theory with dual-phase-lag (DPL) , as well as the coupled thermoelasticity (CTE) theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P-and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.