Blade-hub dynamics of a horizontal-axis wind turbine is studied. Blade equations are coupled through the hub equation, and have parametric terms due to cyclic aerodynamic forces, centrifugal effects and gravitational forces. Blade inertia is usually small compared to the rotor inertia, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By doing so, and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using method of multiple scales. The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude frequency relations and stabilities of these resonances are studied.
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