弹性约束边界圆环板面内自由振动的二维弹性解

摘要

Based on the two-dimension theory of linear elasticity and applying Hamilton's principle,the in-plane free vibration of governing differential equations for annular plates are obtained.Applying differential quadrature method (DQM),the frequencies of in-plane free vibration of annular plates with elastically restrained edges are investigated.All the classical boundary for in-plane displacements can be simulated by setting the stiffnesses of the restraining springs to either zero or infinite.The results presented in this paper has illustrated the analytical method was effective and accurate by comparison of previously reported results with those published in literatures.Finally,The influence of the boundary conditions,geometrical parameter,and stiffness coefficients on the dimensionless frequencies of the annular plates are fully investigated.%基于二维线弹性理论，应用哈密顿原理导出弹性约束边界圆环板面内自由振动的控制微分方程。采用微分求积法(DQM)数值研究了弹性约束边界圆环板面内自由振动的频率特性。通过设置弹性刚度系数为0或∞，问题退化为四种典型边界圆环板的面内自由振动，与已有文献的计算数值结果进行比较，证实本文的分析求解方法行之有效。最后全面考虑了圆环板边界条件、几何系数及刚度系数对自振频率的影响。