Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation,ZAMM - Journal of Applied Mathematics and Mechanics

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Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-07-05 , DOI: 10.1002/zamm.201900267
Nantu Sarkar ₁ , Sudip Mondal ₂

Affiliation

The present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. 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 obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

中文翻译：

具有两个温度公式的改进格林-林赛模型下的热弹性平面波

本研究涉及在修正的格林-林赛广义广义热弹性理论的二温修正框架下，热弹性平面波从均匀，各向同性导热弹性半空间的无应力和绝热表面反射和传播的问题。（2TMGL）。热弹性耦合效应产生两种类型的耦合纵波，它们既分散又衰减。与热弹性耦合效应不同，还存在一个独立的垂直剪切型（SV型）波。与经典的格林—林赛（GL）和洛德·舒尔曼（LS）的广义热弹性理论相反，SV型波不仅在自然界中是弥散性的，而且会衰减。当使耦合纵波入射到自由表面上时，确定反射热弹性波的振幅比及其各自的能量比的解析表达式。本文以特定参数选择的相位速度，振幅比及其各自的能量比的数值结果作为结束。已经绘制了各种图形来分析这些量的行为。通过将本模型获得的数值结果与双温度格林－林赛（2TGL）和双温度Lord-Shulman（2TLS）模型获得的数值结果进行比较，讨论了采用2TMGL模型的特征。本文以特定参数选择的相位速度，振幅比及其各自的能量比的数值结果作为结束。已经绘制了各种图形来分析这些量的行为。通过将本模型获得的数值结果与双温度格林－林赛（2TGL）和双温度Lord-Shulman（2TLS）模型获得的数值结果进行比较，讨论了采用2TMGL模型的特征。本文以特定参数选择的相位速度，振幅比及其各自的能量比的数值结果作为结束。已经绘制了各种图形来分析这些量的行为。通过将本模型获得的数值结果与双温度格林－林赛（2TGL）和双温度Lord-Shulman（2TLS）模型获得的数值结果进行比较，讨论了采用2TMGL模型的特征。

更新日期：2020-07-05

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