In this work, the out-of-plane equation of motion of a wind turbine blade modeled as a beam is developed using the Lagrange formulation. The modeling of aerodynamic loads is done with the blade element momentum theory. The equation of motion has combined effects of parametric and direct excitations and is reduced to a single mode. Perturbation analysis based on previous work shows how various terms affect the steady-state responses near resonance. Numerical simulations using parameters from a real turbine, reveal that these resonance become critical as the blades increase in size. The out-of-plane vibration model shows resonances that would not be expected by blade designers without analysis and modeling techniques presented in this work. The influence of these superharmonic blade vibration responses on the increased loads on the gearbox components would provide insight into premature failure of wind turbine blades and gearboxes.

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