The focus of this paper is on the propagation of thermoelastic waves with assigned wavelength within the context of theory of thermoelasticity for materials with double porosity. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system or by thermal effects. Furthermore, there also exist other four longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes and one quasi-thermal mode. The dispersion relation is explicitly established like a fifth degree algebraic equation with real coefficients and hence it always allows some real roots, thus predicting existence of some standing waves. A numerical analysis for Berea sandstone shows that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elastic model or that in the double porosity elastic model. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established. As an illustrative example it is used Berea sandstone when the secular equation is solved by means of the graphical method to prove that the Rayleigh surface wave problem admits a solution.

本文的重点是在具有双孔隙率的材料的热弹性理论的背景下，传播具有指定波长的热弹性波。结果表明，存在两个剪切波，它们在时间上没有衰减，没有分散，并且由于孔隙系统的存在或热效应而没有改变。此外，还存在其他四个在时间上具有色散和衰减的纵向波解：一个纵向准弹性波，两个准孔模和一个准热模。色散关系像具有实系数的五次代数方程一样被明确建立，因此它总是允许某些实根，从而预测某些驻波的存在。对Berea砂岩的数值分析表明，纵向准弹性波的传播速度大于经典弹性模型或双孔隙弹性模型中对应纵向波的传播速度。解决了瑞利面波的传播问题，并明确建立了相应的长期方程。作为一个说明性示例，当通过图形方法求解长期方程时，使用Berea砂岩来证明瑞利面波问题可以解决。