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The coupling model between the turbine blades with a varying rotating speed and oncoming vortices is constructed, where the coupling of the structure and the fluid is simulated by the van der Pol oscillation. The partial differential governing equations of motions for the coupled system are obtained and discretized by using the Galerkin method. The 1:2 subharmonic resonance and the 1:3 internal resonance are investigated with the multiple scale method and the first-order averaged equations are then derived. The nonlinear responses and bifurcation characteristics are studied by the numerical integration method. The stabilities of the bifurcation curves are determined by utilizing the Routh-Hurwitz criterion. The effects of system parameters including the detuning parameter, the steady-state rotating speed, the amplitude of the periodic perturbation for the rotating speed and the freestream velocity on the vibration responses are investigated.