We consider a magnetothermoelastic problem for a non-homogeneous, isotropic rotating hollow cylinder in the context of three theories of generalized formulations, the classical dynamical coupled (CD) theory, the Lord and Shulman's (L-S) theory with one relaxation time parameter as well as the Green and Lindsay's (G-L) theory with two relaxation time parameters. The inner surface of the cylinder is assumed to be traction free and subjected to a time-dependent exponential order thermal shock, whereas the temperature gradient and radial stress component are taken to be zero at the outer surface. The problem is solved numerically using the finite difference method by developing a Crank-Nicolson implicit scheme. The effect of the Maxwell stress component and rotation are illustrated graphically in the theory of magnetothermoelasticity. The computations of the displacement component, temperature distribution, radial and hoop stresses have been estimated. Furthermore, we have validated our numerical results with the results of the existing literature. The study shows that the rotational parameter with larger values has significant effects on the displacement, temperature distribution, and stress components. Thus the study predicts that the material has to be strong at the surface of the inner cylinder when it is in a rotating system.

我们在广义公式的三种理论、经典动力耦合 (CD) 理论、具有一个弛豫时间参数的 Lord 和 Shulman (LS) 理论以及具有两个弛豫时间参数的格林和林赛 (GL) 理论。假设圆柱的内表面是无牵引力的，并受到时间相关的指数级热冲击，而外表面的温度梯度和径向应力分量被认为为零。通过开发 Crank-Nicolson 隐式方案，使用有限差分法对问题进行数值求解。麦克斯韦应力分量和旋转的影响在磁热弹性理论中得到了图解说明。位移分量、温度分布、径向和环向应力的计算已被估计。此外，我们用现有文献的结果验证了我们的数值结果。研究表明，较大的旋转参数对位移、温度分布和应力分量有显着影响。因此，该研究预测，当材料处于旋转系统中时，内圆柱表面的材料必须是坚固的。和应力分量。因此，该研究预测，当材料处于旋转系统中时，内圆柱表面的材料必须是坚固的。和应力分量。因此，该研究预测，当材料处于旋转系统中时，内圆柱表面的材料必须是坚固的。