In this study, the effect of the magnetic field on the thermo-elastic response of a rotating non-uniform circular disk of functionally graded material (FGM) is investigated for both steady and transient states of temperature. A single second-order ordinary differential equation of motion was developed for an FGM disk and solved along with the boundary conditions using the finite-difference method (FDM). The steady-state and transient heat conduction equations were also solved using the finite-difference method. Numerical results were presented and discussed for an Al/Al₂O₃ FGM disk of exponentially varying material properties keeping Poisson’s ratio and magnetic permeability uniform. Displacement and stress components were analyzed by increasing the intensity of the magnetic field for different cases of steady and transient states of temperature. The analysis suggests that the magnetic field has a remarkable effect on the displacement and stress distributions. It is also found that, high intensity of the magnetic field changes the nature and location of maximum stress. The transient analysis of magneto-thermo-elastic field suggests that the increase in the intensity of magnetic field results in the increase in stress intensity near the outer region of the disk and maximum radial stress always exceeds maximum circumferential stress. The effects of inner and outer surface radius, thermal gradient between inner and outer surface, and the outer surface thickness were also analyzed in detail. It was found that, with the decrease in outer surface radius and thermal gradient between inner and outer surface, maximum circumferential stress becomes higher than the maximum radial stress. In addition, the soundness and accuracy of the solutions were verified with the results from the standard computational method and analytical solution.

在这项研究中，针对稳态和瞬态温度，研究了磁场对功能梯度材料（FGM）旋转非均匀圆盘的热弹性响应的影响。为FGM磁盘开发了一个单阶二阶常微分运动方程，并使用有限差分法（FDM）将其与边界条件一起求解。还使用有限差分法求解了稳态和瞬态热传导方程。提出并讨论了Al / Al ₂ O _3的数值结果FGM盘具有指数变化的材料特性，可保持泊松比和磁导率均匀。通过针对不同温度稳态和瞬态情况增加磁场强度来分析位移和应力分量。分析表明，磁场对位移和应力分布有显着影响。还发现，高强度的磁场改变了最大应力的性质和位置。磁热弹性场的瞬态分析表明，磁场强度的增加导致磁盘外部区域附近的应力强度增加，并且最大径向应力始终超过最大圆周应力。内，外表面半径的影响，还详细分析了内外表面之间的热梯度以及外表面厚度。发现，随着外表面半径的减小和内外表面之间的热梯度的减小，最大周向应力变得大于最大径向应力。此外，使用标准计算方法和分析解决方案的结果验证了解决方案的合理性和准确性。