【摘要】 随着系统参数的变化，带有重频的系统可转变成带有密集频率的系统，反之亦然．本文讨论了亏损系统与接近亏损系统之间的关系．并提出了接近亏损系统的平均移位的摄动方法．算例表明了此方法的有效性．更多还原

【Abstract】 The matrix perturbation theory for the distinct eigenvalues of the real symmetric matrix was well developed. If some of eigenvalues are multiple, the nature of the problem changes and difficulties arise. To avoid such difficulties, it is usually assumed that the system has a set of complete eigenvectors to span the space, i.e. the system is non defective. However, in actual engineering problems, such as general damping systems, flutter analysis of aero elasticity, and so on, the defective system, that do not have a set of complete eigenvectors to span the space, do exist and can not be ignored. Recently, Ref. discussed the perturbation method for the defective system. From the numerical examples it can be seen that the system with defective repeated eiganvalues can be transformed into that with close eigenvalues and the corresponding eigenvectors to be near parallel with each other, which is known as the near defective system. Therefore, development of the perturbation theory for the near defective systems with close eigenvalues is necessary. It should be point out that the matrix perturbation methods discussed above for the distinct eigenvalues and repeated eigenvalues can not be used to deal with the case of systems with near defective close eigenvalues. In Ref., using the shift method, the perturbation problem with close eigenvalues for the real modes can be transformed into one of the repeated eigenvalues, which is applicable only for the case of the non defective systems. In this paper, we try to expand the method for perturbation analysis of close eigenvalues in Ref. to the case of near defective systems. First, we discuss the identification of the close eigenvalues and then give matrix perturbation for near defective systems. In order to illustrate the application of the theory discussed, a numerical example is given.更多还原