功能梯度旋转圆板的热弹性固有振动

在考虑热因素及旋转运动条件下，针对金属－陶瓷功能梯度圆板的固有振动问题进行研究．给出随温度变化且材料组分沿厚度方向按幂律分布的材料物性参数，依据热弹性理论得到圆板的能量关系式．基于哈密顿原理建立旋转金属－陶瓷功能梯度圆板热弹性动力学方程．采用伽辽金法得到边界约束下圆板的自由振动方程，确定了静挠度及固有振动频率．基于数值计算，得到系统固有频率值随体积分数指数、转速和温度等参量的变化曲线，讨论了静挠度变化规律及动力系统的奇点稳定性问题．结果表明，固有频率随体积分数指数、材料表面温度以及转速的增加而减小．

Thermoelastic Natural Vibration of a Rotating Functionally Graded Circular Plates

Considering the thermal effect and the rotating motion, the natural vibration of a metal-ceramic functionally graded circular plate is studied. The material parameters are assumed to be temperature dependent and vary in a power law along the thickness direction. Based on the thermoelastic theory, the energy relation of the circular plate is obtained, and the thermo-elastic dynamical equations of the rotating metal-ceramic functionally graded circular plate are derived using Hamiltonian principle.  For the peripheral clamped boundary condition, the free vibration equation of the system is obtained by using the variable separation method and the Galerkin method, and the static deflection and natural vibration frequency are given. Through the numerical calculations, the variation of the natural frequency of the system with the volume fraction index, the rotating speed and the temperature is given. The variation of the static deflection and the singularity stability of the dynamic system are discussed. The results show that the natural frequency of the system decreases with the increase of the volume fraction index, the surface temperature and the rotating speed, respectively.