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.