In the present paper, the governing equations for two-temperature generalized porothermoelasticity are formulated in accordance with Green and Naghdi theory of thermoelasticity without energy dissipation. Two-dimensional plane wave solution of these governing equations indicates the existence of one shear vertical and four coupled longitudinal waves in porothermoelastic medium. A problem on reflection of longitudinal and shear waves is considered at a thermally insulated and stress-free surface of a generalized porothermoelastic solid half-space. The appropriate potentials for incident and reflected waves satisfy the required boundary conditions at free surface of the half-space and a non-homogeneous system of five equations in reflection coefficients is obtained. The expressions for energy ratios of reflected waves are obtained for incidence of both longitudinal and shear waves. The numerical results are obtained for values of porosity lying between 0.01 and 0.5, which are suitable for most of rocks present in the earth’s crust. The experimental data of kerosene-saturated sandstone are selected for numerical computations to observe the effects of two-temperature parameters and porosity on the energy ratios of reflected waves.

中文翻译：

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两温热弹性中的波传播

在本文中，根据Green和Naghdi的无能量耗散热弹性理论，建立了两温度广义多孔热弹性的控制方程。这些控制方程的二维平面波解表明多孔热弹性介质中存在一个垂直剪切波和四个耦合纵波。在广义多孔热弹性固体半空间的绝热和无应力表面上考虑纵波和横波的反射问题。入射波和反射波的合适势能满足半空间自由表面所需的边界条件，得到反射系数的五个方程的非齐次系统。获得了纵波和横波入射时反射波能量比的表达式。数值结果是针对孔隙度介于 0.01 和 0.5 之间的值获得的，这适用于地壳中存在的大多数岩石。选取煤油饱和砂岩的实验数据进行数值计算，观察两温参数和孔隙度对反射波能量比的影响。