功能梯度圆板的轴对称自由振动  

Free Axisymmetric Vibration of FGM Circular Plates

作　　者：王云[1,2] 徐荣桥[1] 丁皓江[1] 

机构地区：[1]浙江大学土木系,紫金港校区,杭州310058 [2]杭州电子科技大学机械工程学院,杭州310018

出　　处：《应用数学和力学》2009年第9期1009-1014,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1087218010725210)

摘　　要：基于三维弹性理论,用直接位移法求解了横观各向同性功能梯度圆板的轴对称自由振动,其材料特性沿板厚度方向按指数形式变化.在弹性简支和刚性滑动两种边界条件下得到了三维精确解,即它逐点满足基本方程和边界条件.最后给出了数值算例并与以前的工作进行了对比.该方法也可推广应用于材料特性沿板厚度任意变化情形.Based on three-dimensional theory, a direct displacement method was presented to investigate free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and its properties obey the exponential law along the thickness of the plate. For two boundary conditions the solution satisfies all basic equations and corresponding boundary condition at every point and thus is three-dimensionaUy exact. Numerical examples were finally tabulated and compared with those of previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness of the plate.

关 键 词：功能梯度材料 圆板 自由振动 轴对称 

分 类 号：O343.1[理学—固体力学]