非比例阻尼结构复模态问题求解的矩阵摄动法

Matrix Perturbation Method for Solving the Complex Modal Problem of Non-proportionally Damped Structures

建立了一种改进的矩阵摄动法来求解非比例阻尼结构体系的复模态特征值问题，即利用原体系无阻尼实模态问题的解，把实模态变换后的模态阻尼矩阵分解成比例和纯非比例两部分，以此定义一个摄动参数，运用摄动分析方法简捷地得到体系的复模态特征对的摄动解．该方法可根据需要求解所需的前任意阶特征对，求解效果好，而且它适用于强、弱非比例阻尼情况，也可用于非对称阵阻尼矩阵体系的复模态特征值问题的分析．

A modified matrix perturbation method is developed for solving the complex modal eigenvalue problem of non-proportionally damped structural systems. By using eigenproblem solutions of the undamped system, the modal damping matrix is decomposed into proportional and purely non-proportional terms after transforming into the modal co-ordinates. Furthermore, a perturbation quantity is defined; and then by the matrix perturbation method, a set of perturbation solutions of the complex modal eigenvalue problem can be solved rapidly. This method can efficiently determine some or all of the system complex eigenvalue and eigenveetor pairs with required accuracy. The method is suitable for the eigenproblem analysis of lightly and strongly non-proportional damping systems as well as unsymmetric damping matrix systems.