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In this paper,a nonlinear rotor with viscous damping and external periodicexcitation are investigated.The analytical solutions of in close form of this nonlinear rotor are obtained for the free vibration and the forced vibration cases.The numerical simulations are carried out to verify the theory analysis.Comparison shows that the theoretical and numerical results are in good agreement.These theoretical results advocate further investigation of the parameter of structure design of nonlinear rotor model in the engineering application.