Reflection and Refraction of P Wave at the Interface Between Thermoelastic and Porous Thermoelastic Medium

Reflection and refraction phenomenon due to an obliquely incident longitudinal wave at a plane interface between an isotropic, homogeneous, thermoelastic medium and a porous thermoelastic medium is studied. Firstly, the generalized thermoelastic theory (G-TE) of wave propagation in a saturated porous thermoelastic medium is developed in the context of the coupled thermoelastic theories of Biot, the theory of generalized thermoelasticity of Lord–Shulman (with one relaxation time) and that of Green–Lindsay (with two relaxation times). Then, the expressions of amplitude ratios of various reflected and refracted waves to that of incident P wave are derived. Numerical results are obtained and used to analyze the difference of reflection amplitude of four kinds of reflection waves, and refraction amplitude of three kinds of refraction waves among the G-TE theory, the Lord–Shulman theory and the Green–Lindsay theory in the case of porous thermoelasticity. The effect of relaxation time τ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{_1} $$\end{document} and thermal expansion coefficient as\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_\mathrm{s}$$\end{document} on the reflection and refraction of the incident P-wave is also discussed.