四边弹性约束FGM矩形板面内自由振动的DQM求解

发布时间：2018-05-31 09:10

本文选题：FGM矩形板 + 面内自由振动　；参考：《振动与冲击》2016年17期

【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。
[Abstract]:It is assumed that the rectangular plate is orthotropic and the material property is continuously distributed along the width of the rectangular plate according to the power law. Based on the two-dimensional linear elastic theory, the control partial differential equation of the free vibration in the rectangular plate surface of Functionally Graded Material, FGM is established. The control equation is a complex coupling variable coefficient. Partial differential equations, using the differential quadrature method (Differential Quadrature Method, DQM) to study the dimensionless frequency characteristics of free vibration in a rectangular plate surface with quadrangular elastic constraints. By setting the elastic stiffness coefficient of 0 or infinity, the gradient index is 0, the problem is degenerated into the free vibration of a rectangular plate under a variety of canonical boundaries. The results of the vibration frequency of the isotropic rectangular plate are compared, and the results show that the analytical solution is effective. Finally, the influence of the boundary conditions of the FGM rectangular plate, the ratio of length to width, the gradient index and the stiffness coefficient on the frequency of the vibration are considered.
【作者单位】：兰州工业学院土木工程学院;兰州理工大学理学院工程力学系;
【基金】：国家自然科学基金(41202230) 甘肃省自然科学基金(148RJZA017)
【分类号】：O343;O327

【参考文献】