PERTURBATION ANALYSIS OF VIBRATION MODES WITH CLOSE FREQUENCIES

This paper focuses on how parameter changes in a vibration system expr essed by a discrete eigenvalue problem affect vibration modes in the s pecial case of closely spaced eigenvalues, i.e. 'eigenvalue clusters'. For this class of problems, a perturbation analysis is developed that can be used to compute changes in eigenvalues and eigenvectors in res ponse to small parameter changes. The analysis is applied to a 6-degre e-of-freedom spring-mass system containing a single pair of closely sp aced eigenvalues.