大型机械动力学设计的复模态矩阵摄动法

Matrix Perturbation Method for Complex Modes with Repeated Eigenvalues

针对现有的大型机械动力学设计的复模态矩阵摄动法不能简单地唯一确定特征向量的所有摄动系数这一缺陷，作者在文［１］中通过引进一个简单的范化条件，导出了孤立复特征值情况的复模态矩阵摄动公式。但该法对系统存在重特征值时失效。为此，本文进一步研究了重特征值的复模态矩阵摄动法，详细导出了相应的摄动公式。

There exists an imperfection that the perturbation terms of eigenvectors can not be uniquely determined by the now available matrix perturbation methods for comples modes. In Ref., by introducing simple normalization conditions, the perturbation formulae have been completely derived for the case of distinct complex eigenvalues. Yet for practical structures, the case of repeated complex eigenvalues often need to be dealt with. To this end, in the present paper, the same normalization conditions are employed and the uncertain perturbation coefficients of eigenvectors for the repeated eigenvalues are conveniently determined. As a result, the whole perturbation formulae are derived. This paper is a continuation of Ref. and a further supplement to matrix perturbation method for complex modes.