一维结构系统重频特征问题的摄动传递矩阵法

基于传递矩阵法，给出一维结构系统重频振动特征问题的二阶摄动计算方法，该方法适用于一般的一维结构系统的实数和复数重频振动特征问题的摄动分析，并且可避免模态截断误差的影响。只要知道某阶重频的特征值和它的特征向量，用该方法便可准确地计算出其特征值和特征向量的一阶与二阶摄动。算例对弹性支承梁的复数重频振动特征问题进行摄动分析，摄动计算结果和精确计算结果吻合良好。

PERTURBATION TRANSFER MATRIX METHOD FOR ONE-DIMENSIONAL STRUCTURAL SYSTEM WITH REPEATED EIGENVALUES

A general method based on transfer matrix method is presented to calculate the 2nd order perturbations of eigendatas for one-dimensional structural system with repeated eigenvalues. By making singular value decomposition, the equations that contain the unknown perturbing eigenvalues and unknown perturbing eigenvectors were solved accurately. The method is applicable to both real and complex eigendatas of any one-dimensional structural system, and the errors caused by truncating the high modals are avoided. As long as the repeated eigenvalue and corresponding eigenvectors are given, their 1st and 2nd order perturbations can be calculated accurately, and the other eigenvalues and eigenvectors are not needed. The method was applied to the perturbation analysis of the repeated eigenvalues for a beam elastically supported at both ends, and the differences between the perturbation results and the accurate calculating results were small.