The effect of viscosity and hyperbolic two-temperature on energy ratios in elastic and piezoviscothermoelastic half-spaces

This paper reports the behavior of plane wave propagation through the interface of an elastic half-space (ES) and a transversely isotropic piezoviscothermoelastic half-space composed of dual phase lag and hyperbolic two-temperature (PTHD). Two waves are reflected when P waves move longitudinally, or SV waves move transversally to reach the ES medium, and the four waves are transmitted through the PTHD medium. The amplitude ratios for reflected and transmitted waves are determined by satisfying the boundary conditions. These ratios are subsequently utilized to calculate energy ratios for those waves. The effects of viscosity, hyperbolic two-temperature (HTT), classical two-temperature (CTT), and one-temperature (OTT) on the energy ratios are analyzed. The balance of energy conservation is analyzed for some cases.