Abstract

The main concern of this article is to deal with the thermoelastic interaction in a functionally graded thermoelastic rod being enlightened by the memory-dependent derivative. This article investigates the transient phenomena due to the influence of an induced magnetic field of constant intensity and due to the presence of a moving heat source of constant velocity in the context of three-phase lag model of generalized thermoelasticity. Employing the Laplace and the Fourier transforms as tool, the problem has been constructed in the transformed domain. The inversions of the Fourier transform have been carried out using residual calculus whereas the numerical inversions of the Laplace transform have been performed employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod are carried out and have been demonstrated graphically. The results also demonstrate how the nonhomogeneity parameter and the speed of the moving heat source influence the thermophysical quantities. It is observed that the temperature, thermally induced displacement, and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, nonhomogeneity, and memory effect also.

摘要

本文的主要关注点是处理功能梯度热弹性棒中的热弹性相互作用，该棒受到记忆相关导数的启发。本文在广义热弹性三相滞后模型的背景下，研究了由于恒定强度的感应磁场的影响以及由于存在恒定速度的移动热源而导致的瞬态现象。使用拉普拉斯变换和傅里叶变换作为工具，问题已在变换域中构建。傅里叶变换的反演是使用剩余微积分进行的，而拉普拉斯变换的数值反演是使用黎曼求和近似法进行的。应力、位移的数值计算，棒内的温度和温度进行了计算，并以图形方式进行了演示。结果还证明了非均匀性参数和移动热源的速度如何影响热物理量。据观察，发现棒的温度、热致位移和应力在大源速度下降低。此外，由于磁场、非均匀性和记忆效应的影响，还揭示了热物理量的显着差异。