A Numerical Method for Free Vibration Analysis of Structures with Small Design Changes

Abstract

Small design changes are usually repeated at design phase of structures, and it appears to be of practical significance to develop effective numerical methods for analysis of free vibration problems of structures with small perturbations. This paper presents a numerical method for perturbation analysis of matrix eigenvalue problems, where the eigenpairs necessary to be considered are assumed to be non-degenerate in unperturbed states. The proposed method is based on an iteration scheme combined with the use of generalized inverses of singular matrices. The scheme is designed to be easily implemented on large-scale finite element programs. To see effectiveness and fundamental properties of the proposed method, some numerical results are given for lateral vibrations of cantilever beams and circular plates.