四边弹性约束FGM矩形板面内自由振动的DQM求解

摘要

假设矩形板为正交各向异性，材料的物性沿矩形板的宽度方向按幂律连续分布，基于二维线弹性理论，建立了四边弹性约束功能梯度材料（Functionally Graded Material，FGM）矩形板面内自由振动的控制偏微分方程。控制方程为复杂耦合的变系数偏微分方程，采用微分求积法（Differential Quadrature Method，DQM）数值研究了四边弹性约束FGM矩形板面内自由振动的无量纲频率特性。通过设置弹性刚度系数为0或∞，梯度指数为0，问题退化为各种典型边界下矩形板的面内自由振动，与已有的各向同性矩形板自振频率结果进行比较，结果表明分析求解方法行之有效。最后考虑了FGM矩形板边界条件、长宽比、梯度指数及刚度系数对自振频率的影响。%The material of rectangular plates was assumed to be orthotropic,and material properties change continuously along the width of a rectangular plate according to power law distributions.Based on the two-dimension theory of linear elasticity,the governing partial differential equations for in-plane free vibration of FGM rectangular plates with 4 elastically restrained edges were derived.The partial differential equations were complicated and coupled with variable coefficients.Using the differential quadrature method,dimensionless frequency characteristics of in-plane free vibration of FGM rectangular plates with 4 elastically restrained edges were investigated.All the typical boundaries for in-plane vibration of isotropic rectangular plates were obtained by setting stiffnesses of restraining springs to be either zero or infinite and taking material gradient index as zero.Then,the results with DQM were compared with those published in literature for isotropic rectangular plates,it was shwon that the proposed DQM is effective.Finally,The influences of boundary conditions,geometrical parameters,material gradient index and stiffness coefficients on the natural frequencies of FGM rectangular plates were analyzed.