FGM圆环板面内自由振动的DQM求解

基于二维线弹性理论,假定材料物性沿圆环板的径向按照幂律梯度分布,建立了FGM薄圆环板面内自由振动的运动微分方程,采用微分求积法数值研究了FGM圆环板面内自由振动的量纲一频率特性,并与各向同性材料圆环板面内自由振动的量纲一频率进行了比较,说明本文的分析方法有效. 结果表明,不同边界条件,FGM梯度指标以及FGM圆环板内、外半径比对量纲一频率均有影响,其计算结果和分析方法可供设计参考. 

In-Plane Free Vibration Analysis for FGM Annular Plates by Differential Quadrature Method

Based on the two-dimensional linear elastic theory and on the assumption that the material properties vary with power law in the radial direction of annular plates, a differential motion equation of in-plane free vibration was established for the functionally graded material(FGM)thin annular plates. With the differential quadrature method (DQM), the dimensionless frequency parameters of in-plane free vibration of the FGM annular plates were investigated numerically. Compared with the dimensionless frequency of isotropic annular plates, the formulations presented in this paper were validated. The results show that the different boundary condition, material property graded index and the inner to outer radial ratio of the FGM annular plates affect on the dimensionless frequency parameters. The results and the formulations will be a reference for design.