Abstract The present article investigates a new mathematical model of generalized thermo-viscoelasticity based on memory-dependent derivative in the context of three-phase-lag heat transfer subjected to an instantaneous point heat source. The governing coupled equations associated with kernel function and time delay are constituted for a two-dimensional problem of semi-infinite space in an isotropic medium. The bounding surface of the half-space is assumed to be subjected to a time-dependent thermal shock and rigidly fixed. The Eigenfunction expansion approach is proposed to analyze the problem and, consequently, the analytical solutions of the thermodynamic field variables viz. temperature, displacement and stresses are obtained in the Laplace-Fourier transformed domain. The effects of the kernel function and time-delay factor on the distributions of the non-dimensional thermodynamic field variables are presented graphically and compared with the several well-known generalized thermoelasticity theories present in the literature. Finally, some remarkable points are mentioned in conclusion.

中文翻译：

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由于三相滞后传热，具有记忆相关导数的广义热粘弹性特征函数方法

摘要 本文在瞬时点热源作用下的三相滞后传热背景下，研究了基于记忆相关导数的广义热粘弹性新数学模型。针对各向同性介质中半无限空间的二维问题，构造了与核函数和时滞相关的控制耦合方程。假设半空间的边界面受到与时间相关的热冲击并严格固定。提出了本征函数展开方法来分析问题，从而得到热力学场变量的解析解，即。在拉普拉斯-傅立叶变换域中获得温度、位移和应力。核函数和时滞因子对无量纲热力学场变量分布的影响以图形方式呈现，并与文献中存在的几个众所周知的广义热弹性理论进行了比较。最后，在结论中提到了一些值得注意的地方。