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This paper presents a new effective approach to solving the generalized eigenvalue problem Bu =Mu by using a perturbation technique. A generalized second-order perturbation theory is adapted such that the perturbed solution will be based on the eigensolution of an unperturbed subproblem describing the conservative part of the original nonclassically, viscously damped system with asymmetric mass, damping and stiffness matrices. Two numerical examples in addition to a practical problem are studied to show that tk eigensolutions obtained by the current method match, to a great ex?ent, so!utions obtained by time-consuming exact methods.

EIGENSOLUTION OF NONCLASSICALLY DAMPED ASYMMETRIC VIBRATION SYSTEMS