四边弹性约束矩形板面内自由振动的 DQM求解

摘要

Based on the two-dimension theory of linear elasticity and an application of the Hamilton's principle,the in-plane free vibration of governing partial differential equations for rectangular plates with elastically restrained edges is derived.Using the differential quadrature method (DQM),the dimensionless frequencies of in-plane free vibration of rectangular plates with elastically restrained edges are investigated.All the classical boundaries for in-plane displacements can be simulated by setting the stiffnesses of the restraining springs to either zero or infinite.The application of DQMin this paper has illustrated that the analytical method was validated and accurate by comparison with previously reported results and those available in the literature for rectangular plates.Finally,the influence of the boundary conditions,geometrical parameter,and stiffness coefficients on the dimensionless frequencies of the rectangular plates are investigated.%基于二维线弹性理论，应用 Halmiton 原理，建立了四边弹性约束边界矩形板面内自由振动的控制偏微分方程。采用微分求积法（DQM）数值研究了弹性约束边界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∞，问题退化为各种典型边界矩形板的面内自由振动，与已有的矩形板面内自振频率结果进行比较，结果显示，该分析求解方法行之有效；最后考虑了矩形板边界条件、长宽比、刚度系数对自振频率的影响。