Perturbation Technique for Non-Self-Adjoint Systems with Repeated Eigenvalues

Abstract

The reanalysis of non-self-adjoint systems is computationally very expensive in the design of structural dynamics. An effective, even if approximate, evaluation of the eigensolutions of a modified system is valuable to designers. In a paper by Meirovitch and Ryland (Meirovitch, L., and Ryland, G., A Perturbation Technique for Gyroscopic Systems with Small Internal and External Damping,' Journal of Sound and Vibration, Vol. 100, No. 3, 1985, pp. 393408), a perturbation technique was used to derive the perturhed solutions of a damped gyroscopic system with distinct eigenvalues. That approach is extended to the case of systems with repeated eigenvalues. A numerical example is presented to verify the present method, and satisfactory results are observed.