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Relaxation effects on thermoelastic interactions for time-dependent moving heat source under a recent model of thermoelasticity
Zeitschrift für angewandte Mathematik und Physik ( IF 2 ) Pub Date : 2021-01-18 , DOI: 10.1007/s00033-020-01462-x
Robin Vikram Singh , Santwana Mukhopadhyay

In the present article, we investigate the thermal and elastic behaviour of an infinite thermoelastic material with a cylindrical cavity caused by a time-dependent moving heat source. The cavity surface is assumed to be subjected to a thermal shock. The formulation of the problem is applied for the recently proposed generalized thermoelastic model [Modified Green–Lindsay (MGL)] that takes into account the strain and temperature rates in the constitutive relations. We derive the governing equations in the present context along with the other two models, namely Lord–Shulman model and Green–Lindsay, by unifying governing equations under all these three models. The solutions are obtained for all three models in the Laplace transform domain, which are represented by unified expressions. The numerical computations for temperature, displacement and thermal stresses are carried out and depicted graphically. A detailed comparison is made amongst the results predicted by three models to highlight the effects of velocity of heat source and strain, temperature rate terms involved in the MGL model.



中文翻译:

时变运动热源在最新热弹性模型下对热弹性相互作用的弛豫效应

在本文中,我们研究了由时变运动热源引起的无限热弹性材料具有圆柱形空腔的热和弹性行为。假定型腔表面受到热冲击。该问题的提法适用于最近提出的广义热弹性模型[Modified Green-Lindsay(MGL)],该模型考虑了本构关系中的应变和温度速率。通过统一所有这三个模型下的控制方程,我们可以得出本文中的控制方程以及其他两个模型,即Lord-Shulman模型和Green-Lindsay。对于Laplace变换域中的所有三个模型,都获得了解决方案,并用统一的表达式表示。温度的数值计算 进行位移和热应力并以图形方式显示。在三个模型预测的结果之间进行了详细的比较,以突出显示热源速度和应变,MGL模型涉及的温度速率项的影响。

更新日期:2021-01-18
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