Abstract The present study is concerned with the reflection of magneto-thermoelastic plane waves from stress free and thermally insulated surface in a homogeneous isotropic thermally conducting elastic half-space medium. The modified Green–Lindsay (MGL) theory of generalized thermoelasticity has employed with two temperatures (2 T). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. There exist also due to the thermoelastic coupling one independent vertically shear (SV-wave) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the reflection coefficients and their respective energy ratios for reflected thermoelastic waves have been determined when the coupled longitudinal wave incident on the free surface. A numerical result on the reflection coefficients and their respective energy ratios for the specific parameter has been calculated. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those in the classical GL model.

中文翻译：

---

两种温度下修正的格林-林赛模型下固体半空间磁热弹性波的反射

摘要 本研究涉及均匀各向同性导热弹性半空间介质中无应力且绝热表面的磁热弹性平面波的反射。广义热弹性的修正格林-林赛 (MGL) 理论已在两个温度 (2 T) 下使用。热弹性耦合效应产生两种类型的耦合纵波，它们是色散的和衰减的。由于热弹性耦合，还存在一个独立的垂直剪切（SV 波）波。与广义热弹性的经典格林-林赛 (GL) 和洛德-舒尔曼 (LS) 理论相比，SV 波不仅在本质上是色散的，而且还会经历衰减。确定了耦合纵波入射到自由表面时反射热弹性波的反射系数及其各自能量比的解析表达式。已经计算了特定参数的反射系数和它们各自的能量比的数值结果。绘制了各种图表来分析这些量的行为。通过比较现有模型与经典GL模型的数值结果，讨论了采用2TMGL模型的特点。绘制了各种图表来分析这些量的行为。通过比较现有模型与经典GL模型的数值结果，讨论了采用2TMGL模型的特点。绘制了各种图表来分析这些量的行为。通过比较现有模型与经典GL模型的数值结果，讨论了采用2TMGL模型的特点。