Abstract The present paper concerns with the fundamental solutions for strain and temperature rate-dependent thermoelasticity theory recently developed by Yu et al. (2018). This recently developed model is theoretically established with the aid of principles of thermodynamics and by adding the strain-rate term in temperature rate-dependent thermoelasticity theory, which was proposed by Green and Lindsay (GL)(1972). This model has attempted to remove the drawback of discontinuity in the displacement field under Green-Lindsay (GL) model. We consider this modified Green-Lindsay (MGL) model for the case of homogeneous and isotropic bodies. Two cases, namely, concentrated body force and concentrated heat source have been taken for deriving the fundamental solutions for thermoelasticity in the context of MGL model. The fundamental solutions for the distributions of displacement components and temperature are obtained by the Laplace transform method. Fundamental solutions in the physical domain are obtained by Laplace inversion and the solution of displacement and temperature is obtained for short-time approximation. Lastly, we get the fundamental solution of the system of equations in the case of steady oscillations.

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关于应变和温度速率相关的广义热弹性理论的基本解

摘要 本文关注于最近由 Yu 等人开发的应变和温度速率相关热弹性理论的基本解决方案。(2018)。这个最近开发的模型是在热力学原理的帮助下，通过在 Green 和 Lindsay (GL) (1972) 提出的温度速率相关热弹性理论中添加应变速率项而在理论上建立的。该模型试图消除 Green-Lindsay (GL) 模型下位移场不连续的缺点。对于均质体和各向同性体的情况，我们考虑了这种改进的 Green-Lindsay (MGL) 模型。在 MGL 模型的背景下，采用集中体力和集中热源两种情况来推导热弹性的基本解。位移分量和温度分布的基本解是通过拉普拉斯变换方法获得的。物理域的基本解通过拉普拉斯反演得到，位移和温度的解得到短时间近似。最后，我们得到了方程组在稳态振荡情况下的基本解。