Perturbation analysis of vibration modes with close frequencies

This paper focuses on how parameter changes in a vibration system expressed by a discrete eigenvalue problem affect vibration modes in the special 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 response to small parameter changes. The analysis is applied to a 6‐degree‐of‐freedom spring‐mass system containing a single pair of closely spaced eigenvalues.