变厚度圆板的非线性振动-《郑州大学学报(工学版)》

文章信息/Info

Author(s):: Huang Shitao; Department of Machinery Department of Zhengzhou University of Technology

Keywords:: Deformation round board; nonlinear vibration; finite element method; feature value issues

摘要:: 本文利用有限元的方法研究了变厚度的圆极，在大变形时所作的非线性振动情况。文章首先导出了在一般情况时的非线性偏微分主程及其边界条件。然后，利用结点座标和插入函数重新改写圆板的应变能和动能，再应用Ｈａｍｉｌｔｏｎ原理，获得变厚度圆板在大变形时的矩阵形式的方程。把相应的边界条件强加到该矩阵方程中，以至于该方程满足边界条件。然后，利用递归的方法来解其特征值问题。本文利用一个例子说明了变厚度圆板在作非线性振动时，其基频与振幅之间的关系。其计算结果的精度优于其它方法。该方法可以推广到解其它类似的圆板的非线性振动问题中

Abstract:: This article uses the method of finite element to study the round pole of deformation, and the non -linear vibration conditions made during large deformation. The article first exports the non -linear partial micro -divide and its boundary conditions in general. Then, use the node seat label and insert function to rewrite the strain energy and kinetic energy of the circular plate, and then apply the Hamilton principle to obtain the equation of the matrix form of the thickness round plate when the large deformation is obtained. The corresponding boundary conditions are imposed into the matrix equation so that the equation meets the boundary conditions. Then, the recursion method is used to solve the characteristics of its characteristic value. This article uses an example to illustrate the relationship between the base frequency and amplitude when the thickness of the deformation board is not linear vibration. The accuracy of its calculation results is better than other methods. This method can be promoted to the non -linear vibration problem of other similar round boards.