Abstract

The present study is concerned with the reflection phenomenon of thermoelastic plane waves at the thermally insulated stress-free surface of a homogeneous isotropic thermally conducting elastic half-space in the frame of modified Green-Lindasy (MGL) model of generalized thermoelasticity with strain rate. The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive in nature as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exist one independent vertically shear-type (SV-type) wave. In contrast to the classical Green-Lindsay (GL) and the 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 the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on a 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 are plotted to analyzed the analytical solution. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the MGL model with those obtained in case of the GL, LS and the coupled thermoelasticity (CTE) models.

摘要

本研究涉及热弹性平面波在具有应变率的广义热弹性的修正格林-林达西 (MGL) 模型框架中均匀各向同性导热弹性半空间的绝热无应力表面处的反射现象。热弹性耦合效应产生两种类型的耦合纵波，它们本质上是色散的，也表现出衰减。与热弹性耦合效应不同，还存在一种独立的垂直剪切型（SV型）波。与经典的 Green-Lindsay (GL) 和 Lord-Shulman (LS) 广义热弹性理论相比，SV 型波不仅在性质上是色散的，而且还会经历衰减。当耦合纵波入射到表面上时，确定反射热弹性波的振幅比和它们各自的能量比的解析表达式。本文最后给出了特定参数选择下相位速度、幅度比及其各自能量比的数值结果。绘制了各种图形以分析解析解。通过将 MGL 模型的数值结果与 GL、LS 和耦合热弹性 (CTE) 模型的数值结果进行比较，讨论了采用 MGL 模型的特点。特定参数选择的振幅比及其各自的能量比。绘制了各种图形以分析解析解。通过将 MGL 模型的数值结果与 GL、LS 和耦合热弹性 (CTE) 模型的数值结果进行比较，讨论了采用 MGL 模型的特点。特定参数选择的振幅比及其各自的能量比。绘制了各种图形以分析解析解。通过将 MGL 模型的数值结果与 GL、LS 和耦合热弹性 (CTE) 模型的数值结果进行比较，讨论了采用 MGL 模型的特点。