This paper considers the thermoelastic theory with two temperatures that involves higher gradients of thermal and mechanical effects. The wave propagation question is addressed within the class of waves of assigned wavelength. Considering harmonic in time wave solutions, it is found that the transverse waves are undamped in time and non-dispersive, and they are not altered by the thermal effects. Conversely, the longitudinal waves are dispersive and damped in time; the dispersion relation is established like a cubic equation and the effects of conductive temperature are explicitly presented. Rayleigh surface waves are also studied and an explicit secular equation is derived by using wave solutions damped in time. Illustrative examples are numerically analyzed and graphically depicted. The results achieved are meaningful because they are able to bring information about the propagation of waves with assigned length and, moreover, they are in agreement with the results regarding the wave speed of travelling discontinuities. Also the structure of the wave solutions provides information upon asymptotic stability.

中文翻译：

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两种温度下热弹性理论中的波传播

本文考虑了具有两个温度的热弹性理论，其中涉及更高的热效应和机械效应梯度。波传播问题在指定波长的波类中得到解决。考虑时间波解中的谐波，发现横波在时间上是无阻尼和非色散的，它们不受热效应的影响。相反，纵波在时间上是分散和衰减的；色散关系像三次方程一样建立，并且明确地呈现了导电温度的影响。还研究了瑞利表面波，并通过使用随时间衰减的波解导出了明确的长期方程。说明性的例子进行了数值分析和图形描绘。所获得的结果是有意义的，因为它们能够带来关于指定长度的波传播的信息，而且，它们与关于行进不连续性的波速的结果一致。波解的结构也提供了关于渐近稳定性的信息。