基于物理中面FGM中厚板自由振动的有限元分析

基于物理中面和一阶剪切变形板理论，研究了不同边界条件下功能梯度材料(FGM)中厚板的自由振动问题．假设功能梯度板的材料性质沿厚度方向按幂函数规律连续变化．根据哈密顿原理建立了FGM板有限元形式的自由振动方程，利用MATLAB软件编写程序进行了计算．通过数值算例，讨论了不同边界条件下FGM中厚板的无量纲频率随材料梯度指数和厚宽比的变化情况，并与经典板理论下的频率进行了比较．

Finite Element Analysis for Free Vibration of FGM Medium Plates Based on the Physical Neutral Surface Concept

Based on the physical neutral surface concept and the first-order shear deformation plate theory (FSDT), free vibration of functionally graded material (FGM) medium plates with different boundary conditions is studied. The material properties are assumed to change continuously only in the thickness direction following a power law distribution. Based on Hamilton principle, the finite element forms of free vibration equations are derived and then solved via MATLAB. The natural frequencies of FGM medium plates with different boundary conditions are given for various values of thickness to width ratios and the power law index. Comparison is made with the results based on the classical plate theory (CPT).