Youssef Hamdy M, El-Bary Alaa A, Al-Lehaibi Eman A N
Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt.
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia.
Sci Rep. 2021 Jan 27;11(1):2289. doi: 10.1038/s41598-021-82127-1.
This work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L'Hopital's rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress-strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).
本工作旨在基于机械损伤考量，在双曲型双温度广义热弹性理论框架下研究旋转对热弹性固体球体的影响。因此，基于机械损伤定义构建了一个具有旋转的热弹性、均匀且各向同性固体球体的数学模型。控制方程是在双曲型双温度广义热弹性理论框架下编写的。球体的边界受到热冲击且无体积变形。利用洛必达法则消除了所研究函数在球心处的奇点。数值结果已通过各种机械损伤值、双温度参数和旋转参数值以图形方式表示。双温度参数对所有研究函数都有显著影响。损伤和旋转对变形、位移、应力和应力应变能有重大影响，而它们对传导温度升高和动态温度升高的影响极小。在双曲型双温度理论和单温度理论（洛德 - 舒尔曼模型）中，热波和机械波以有限速度在热弹性体上传播。
