广义特征值摄动问题的一种通用方法

A New Perturbation Method for General Eigenvalue Problem

研究了结构动力分析中广义特征值问题的矩阵摄动法。根据逐次逼近的思想，提出了一种能同时处理孤立特征值、相近特征值及相重特征值三种不同情况的摄动问题的通用方法。推导过程简单，公式紧凑，且具有足够的精度。计算实例证实了本文方法的有效性。

We are almost certain that there doeS not exist any method that is applicable to all throecases of eigenvalue problem in mechanical vibration: (1)distinct frequencies 3 (2)equal frequencies; (3)nearly equal frequencies. Yet for large complicated structures, we need to dealwith all these three cases.In this paper we, using method of condensation in subspace, derive: (a)perturbationeqs. (12) and (14a)for computing eigenvalues; (b)perturbation eqs. (11), (13)and (14b)forcomputing eigenvectors. We feel quite confident that these equations are simple and elegantin form.We present two illustrative examples: (a) a simple system with nearly equal frequencies;(b)a simple system with equal frequencies. The results calculated with our perturbation equations are extremely close to exact results, auguring well that our perturbation methodwill very likely give calculated results sufficiently accurate for engineering purposes in thecase of large complicated structures.