Abstract

Enlightened by the memory dependent derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a rod in the context of three-phase lag theory of thermoelasticity based on Eringen’s nonlocal elasticity. Both ends of the rod were fixed, and heat is insulated. Employing Laplace transform as a tool, the problem was transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain was obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod was carried out and displayed graphically. The effect of the moving heat source speed, time instance, memory dependent derivative, magnetic field and nonlocality on temperature, displacement, and stress was studied. Finally, three animated were added for easy understanding of the effect of moving the heat source on the studied fields. As per authors concern, the concept of the animated has been presented for the first time in this kinds of literature till now.

摘要

受记忆相关导数的启发，本研究涉及一种新的广义热弹性数学模型，以研究在热弹性三相滞后理论的背景下由于磁场和棒中移动热源的影响而引起的瞬态现象基于Eringen 的非局部弹性. 杆的两端固定，隔热。采用拉普拉斯变换作为工具，将问题转化为空间域并进行解析求解。最后，通过应用拉普拉斯逆变换获得实时域中的解。对杆内的温度、位移和应力进行了数值计算，并以图形方式显示。研究了移动热源速度、时间实例、记忆相关导数、磁场和非定域性对温度、位移和应力的影响。最后，添加了三个动画，以便于理解移动热源对研究领域的影响。按照作者的说法，动画的概念迄今在此类文献中还是首次出现。