虚拟弹簧边界Mindlin板的自由振动和屈曲分析

Free vibration and buckling analysis of Mindlin plate with virtual spring boundaries

对于Mindlin板的自由振动和特征屈曲问题,为了用少量结点数求得高精度数值解,并直接求得完整的模态向量,文中使用虚拟弹簧边界作为边界条件的施加方法,运用微分求积有限单元法推导出Mindlin板的自由振动和屈曲特征方程。基于Matlab编程计算多种边界、不同厚度的Mindlin板的自振频率和屈曲因子,并讨论计算方法的收敛性、准确性及计算效率。数值结果表明,虚拟弹簧边界与微分求积有限单元法相结合的数值方法,计算结果准确,且计算效率有所提高。

With regard to the free vibration and eigenvalue buckling of Mindlin plate,in order to obtain high-precision solutions and complete modal vectors with a few nodes,the equations of free vibration and eigenvalue buckling of Mindlin plate were derived by differential quadrature finite element method with virtual spring boundaries as conditions.According to Matlab programming,the natural frequencies and buckling factors of Mindlin plates with various boundaries and different thicknesses were calculated,and the convergence,accuracy and efficiency of the calculation method were discussed.Results show that the combination of virtual spring boundary and differential quadrature finite element method is accurate and can improve the calculation efficiency.