任意非亏损系统特征灵敏度分析的直接摄动法

本文发展了一种任意非亏损系统特征灵敏度分析的二阶段摄动法，将未摄动的问题的解作为零阶近似，把摄动影响作为摄动后问题的高阶修正，经过严格的数学推导，得到了支配高阶修正量的完全方程组。本方法无损知道摄问题的全部特征向量，仅需知被摄模态的特征对。本方法可处理被摄问题具有重特征值，甚至具有等导重特征值这一高度退化极难处理的情况。算例显示了本方法的正确性。

A DIRECT PERTURBATION METHOD FOR EIGENSENSITIVITY ANALYSIS OF ARBITRARY NONDEFECTIVE SYSTEM

In this paper, a second order direct perturbation method for eigensensitivity analysis of arbitrary nondefective system is developed. The eigenvalues and eigenvectors of the unperturbed problem are regarded as zero order approximation of the perturbed eigensolutions, while the perturbation effect is obtained by higher order modification. Based on strict mathematical derivation, a complate set of equations governing the higher order unknowns of the perturbed eigensolutions is established. The method does not require the complete eigenvector set of the unperturbed problem but rather the knowledge of the unperturbed eigenpairs from which the interesting ones stem. The method can deal with the case where the unperturbed problem has repeated eigenvalues. The repeated eigenvalues are even allowed to have equal derivatives, a case that is highly degenerate and is extremely difficult to treat. Numerical example is given to show the validity of the method.