Abstract The propagation and stability (Whitham’s criteria) of harmonic plane waves are described in the context of the hyperbolic two-temperature generalized thermoelasticity in which heat conduction in deformable bodies depends upon the difference between the double derivative of conductive and dynamic temperature. The exact dispersion relation solutions for the longitudinal plane wave are derived analytically. Several characterizations of the wave field, like phase velocity, specific loss, penetration depth, amplitude coefficient factor, and phase shift are examined for the low as well as high frequency asymptotic expansions. For the validity of analytical findings and to study the effect of varying hyperbolic two-temperature parameter on different characterizations, the numerical computation of a particular example is illustrated and displayed graphically. The results of some earlier works have been deduced and discussed from the present investigation as special limiting cases.

中文翻译：

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双曲线二温度广义热弹性下平面波的表征与稳定性

摘要 谐波平面波的传播和稳定性（惠瑟姆准则）是在双曲线双温度广义热弹性的背景下描述的，其中可变形体中的热传导取决于传导温度和动态温度的二重导数之间的差异。纵向平面波的精确色散关系解是通过解析推导出来的。波场的几个特征，如相速度、比损耗、穿透深度、振幅系数因子和相移，都经过了低频和高频渐近扩展的检验。为了分析结果的有效性并研究不同的双曲线双温度参数对不同表征的影响，以图形方式说明和显示特定示例的数值计算。一些早期工作的结果已经从目前的调查中作为特殊限制案例进行了推论和讨论。