【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去。更多还原

【Abstract】 In the paper finite element method for the problem of large amplitute oscillation of annular elastic plate of variable thickness with rigid mass on inside is presented.It can be shown that the equations and associated boundary conditions of motion for a finite amplitute vibration of the annular plate are non-linear and coupling partial differential.The kinetic energy and strain.energy of the plate are rewritten by the coordinates of nodes and interpulating functions in matrix form.Applying Hamilton Principle the equations for the plate in large deformation are obtained. Then,boundary conditions are imposed on vector of nodal field variables,so that the appropriate boundary conditions are satisfied. The eigenvalue problems are solved by iterated method.The relations between the fundamental frequencies and the amplitutes of nonlinear vibrations of a example of the annular plates with variable thickness are obtained. The results are more accurate by finite element method than by other methods.The methed cab be extended to solving similary non-linear vibrations of annular plates.更多还原