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逐步分析了旋转的功能梯度空心及实心长圆柱体问题的解.假设圆柱体的弹性模量和材料密度沿径向呈指数变化,Poisson比为常数.由平衡方程、相容方程、弹性变形理论及应力-应变关系,导出了统一的控制方程.根据超几何函数,求解该二阶微分控制方程,得到旋转功能梯度圆柱体的弹性变形.检验并讨论了圆柱体中的应力与非均质参数、几何、边界条件之间的相互关系.将旋转功能梯度空心及实心圆柱体的分析结果,与旋转均质各向同性圆柱体的结果进行了对比分析.同时,提出了旋转粘弹性圆柱体的粘弹性解,并验证了空心及实心圆柱体中应力与时间参数间的依赖关系.
The solution to the problem of rotating functionally graded hollow cylinders and solid long cylinders is analyzed step by step. Assuming that the elastic modulus and the material density of the cylinder change exponentially in the radial direction, the Poisson ratio is a constant. The equilibrium equation, the compatibility equation, the elastic deformation theory And the stress-strain relationship, a unified control equation is derived.According to the hypergeometric function, the second order differential governing equations are solved to obtain the elastic deformation of the rotating functionally graded cylinder.The stress and inhomogeneous parameters in the cylinder are tested and discussed , Geometry and boundary conditions of the rotating cylindrical viscoelastic cylinder.The results of the analysis of the rotating functionally graded hollow cylinder and the solid cylinder are compared with those of the rotating homogeneous isotropic cylinder.At the same time, Viscoelastic solutions and verify the dependence of stress and time parameters in hollow and solid cylinders.