Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.

本研究受卡普托分数阶导数（Caputo fractional derivative）启发，基于热弹性三相滞后（TPL）理论，针对受磁场与移动热源作用的杆状结构构建广义热弹性新型数学模型，以探究其瞬态现象。杆的两端均固定且热绝缘。本问题采用拉普拉斯变换（Laplace transform）转换至空间域并完成解析求解，最终通过拉普拉斯逆变换（inverse Laplace transform）得到实时域下的解。对杆内的应力、位移与温度开展数值计算并以图形形式展示结果。研究了移动热源速度对温度、应力与位移的影响。结果表明，当热源速度较大时，杆的温度、热诱导位移与应力均会降低。为更好地理解移动热源对各类分布的影响，本文增设了三段动画。