薄板振动特征值问题的一种改进积分方程解法

本文根据一种改进的边界元/有限元混合法求解薄板振动固有频率问题,既避开了标准的边界元法所导致的求解非代数特征值方程的困难,亦能够基本上消除通常的边界元/有限元混合法结果精度受区域内部单元划分影响较大的弊端。文中讨论了迭代算法的收敛问题,并用于薄板固有频率分析。数值结果表明,即便是在域内单元很粗疏划分的情况下,本文的方法仍能给出相当满意的结果。

An Improved Boundary Integral Equation Method for Eigenvalue Problems of Thin Plate Vibration

In this paper, an improved mixed boundary/finite element (BE/FE) method is proposed and applied to the eigenvalue problems of thin plate vibration. By using this approach, the awkward nonalgebraic eigenvalue equations resulted by BEM are avoided and the drawback of interior meshing domination in accuracy occurred in the normal mixed BE/FE method is greatly reduced. The convergence of the proposed iterative algorithm is discussed. Excellent numerical results are contentedly obtained even in cases of very coarse interior mesh.