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This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle. We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory (NREL), to research the effects of the nonlinear f lap-wise vibration characteristics. The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam, and the nonlinear f lap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first. Then, the blade's large- deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force. Lastly, it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method, and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration. The results indicated that the rotational speed of the impeller has a significant impact on blade vibration. When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16. From the amplitude-frequency curve, it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity. Closed phase trajectories in blade nonlinear vibration, exhibiting periodic motion characteristics, are found through phase diagrams and Poincare section diagrams. [ABSTRACT FROM AUTHOR]