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.