Perturbation technique for non-self-adjoint systems with repeated eigenvalues

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 hv 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, 393-408), a perturbation technique was used to derive the perturbed 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.