摘要
提出了一种基于矩阵广义逆的有限元模型动力缩聚移频迭代方法。该方法首先直接从原系统特征方程出发，导出反映系统主、副自由度之间位移关系的动力缩聚矩阵的控制方程，然后给出了相应的迭代求解方法和收敛准则。为了减少求矩阵广义逆的计算工作量，本文给出了一种替代方法，把对一个高阶满阵求逆转化为对一个同阶高度稀疏矩阵求逆。与已有的动力缩聚迭代法相比，本文提出的方法具有两个显著的优点：其一是迭代收敛速度高；其二是通过改变移频量可达到提高收敛速度和使得降阶后模态的动态性能在任意频段上逼近原系统。数值示例表明，本文提出的方法是切实可行的。
Based on the general inverse technique of matrices, an iterative method of dynamic condensation of finite element models with considering shifting frequency is presented in this paper. The constraint equation of the dynamic condensation matrix, which relates the deformations of the master and slave degrees of freedom, is directly derived from the original eigen equation at first. Then an iterative scheme and convergent criterion for the constraint equation is proposed. In order to reduce the computational work of solving the general inverse of matrix, an alternative approach is given. Comparing all the iterative schemes proposed in the past, the present method has two main advantages. One is that the convergence is much higher. The other is that the dynamic characteristics of the condensed system can close to that of any frequency range of original full model by changing the shifting value. Numerical examples demonstrate that the proposed method is feasible.
出处
《应用力学学报》
CAS
CSCD
北大核心
1999年第2期61-67,共7页
Chinese Journal of Applied Mechanics
关键词
有限元建模
动力分析
动力缩聚
迭代
finite element modeling, dynamic analysis, dynamic condensation, model reduction, general inverse.
