Abstract In this paper, the propagation of time-harmonic plane waves is investigated in an infinite elastic solid material by employing the modified Green–Lindsay (MGL) model of generalized thermoelasticity. It is found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type (SV-type) wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the thermoelastic coupling effect. In contrast to the Green–Lindsay (GL) as well as the Lord–Shulman (LS) models, the SV-type wave is not only dispersive in nature but also experiences attenuation. Reflection phenomenon of an incident coupled longitudinal wave from stress-free and thermally insulated boundary surface of a thermoelastic solid half-space is addressed. Using these boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, reflection coefficients and their respective energy ratios. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in the case of the GL model.

中文翻译：

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修正格林-林赛模型下磁热弹性固体中的波

摘要 在本文中，采用广义热弹性的修正格林-林赛 (MGL) 模型研究了时谐平面波在无限弹性固体材料中的传播。发现由两组耦合纵波和一个独立的垂直剪切型（SV型）波组成的三个基本波可能以不同的速度传播。发现耦合波组是分散的、衰减的并且受热弹性耦合效应的影响。与 Green-Lindsay (GL) 以及 Lord-Shulman (LS) 模型相比，SV 型波不仅在本质上是色散的，而且还会经历衰减。解决了来自热弹性固体半空间的无应力和绝热边界表面的入射耦合纵波的反射现象。使用这些边界条件，给出了各种反射系数和它们各自的能量比的公式。对于特定模型，绘制了各种图表以分析相速度、反射系数及其各自能量比的行为。通过将当前模型获得的数值结果与在 GL 模型情况下获得的数值结果进行比较，讨论了采用 MGL 模型的特点。