Abstract

Compared with the fractional order generalized themoelastic theory, the generalized thermoelastic theory based on the memory-dependent derivative has following significant advantages: First, the generalized thermoelastic theory with memory-dependent derivative has more specific physical meanings and can excellently describe that the present state of a system is dependent on its past states; Second, the memory-dependent derivative is based on the integer order calculus, which is more convenient to operate than fractional order model; Particularly, for different kernel functions, the time-dealy factor has different choice to adapt to different specific problems, which makes it greatly possible to describe the real thermoelastic response of medium. In present work, the transient response of an infinite rotating hollow cylindrical conductor with variable material properties subjected to a thermal shock at its inner surface is investigated based on the generalized thermoelastic theory with memory-dependent derivative. The hollow cylinder is placed in an external magnetic field with constant intensity, whose outer surface is traction free. The governing equations are formulated and then solved by using Laplace transform and its numerical inversion. The distributions of the dimensionless temperature, displacement, induced electric field, induced magnetic field, hoop stress as well as radial stress in the cylinder are obtained and illustrated graphically. The obtained results show that the kernel function, the time-delay factor and the temperature-dependent material properties influence the distributions of the considered variables more or less, while, the angular velocity significantly influence the variations of the dimensionless displacement, hoop stress and radial stress.

摘要

与分数阶广义热弹性理论相比，基于记忆相关导数的广义热弹性理论具有以下显着优势：首先，具有记忆相关导数的广义热弹性理论具有更具体的物理意义，可以很好地描述当前状态一个系统依赖于它过去的状态；二是记忆相关导数基于整数阶微积分，比分数阶模型更便于操作；特别是对于不同的核函数，时效因子有不同的选择以适应不同的具体问题，这使得描述介质真实的热弹性响应成为可能。在目前的工作中，基于具有记忆相关导数的广义热弹性理论，研究了具有可变材料特性的无限旋转空心圆柱导体在内表面受到热冲击的瞬态响应。空心圆柱体置于强度恒定的外部磁场中，其外表面无牵引力。制定控制方程，然后使用拉普拉斯变换及其数值反演求解。获得了圆柱体中无量纲温度、位移、感应电场、感应磁场、环向应力以及径向应力的分布，并以图形方式说明。得到的结果表明，核函数，