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| Analysis of Non-linear Flap Vibration of Wind Turbine Blades |
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Abstract The nonlinear governing equation of flap vibration is established by considering the blade as a rotating Euler-Bernoulli cantilever beam with variable sections on the hub. The unsteady aerodynamic forces acting on the blade are derived by using the Greenberg’s expressions. The assumed-modes method is introduced to compute modes functions since bending rigidity and line density are variable alone the elastic axis and expressions of modes can’t be derived directly. By using these modes functions as a functional base, the Galerkin procedure is applied to the governing equation to discrete the continuum Model. The dynamic response is analyzed by decomposing the flap vibration as static displacements and dynamic displacements. Influences of the rotating speed, the wind velocity, and the rotating angle to flap characteristics are discussed. The study shows that: 1) the influence of the rotating speed to vibration characteristic is dramatic, but those of the wind velocity and the rotating angle are inapparent; 2) the static displacement increases proportionally with the wind velocity, but the aerodynamic damping decreases with the wind velocity; 3) the nonlinear flap vibration under lower wind velocity is attenuating, and it becomes a quasi-periodic vibration through a periodic vibration with increase of the wind velocity.
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Received: 08 October 2010
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2012, Vol. 33 