Non-linear dynamics of wind turbine wings |
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Authors: | J.W. Larsen S.R.K. Nielsen |
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Affiliation: | Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark |
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Abstract: | The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis. Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency ω. Assuming that the fundamental blade and edgewise eigenfrequencies have the ratio of ω2/ω1?2, internal resonances between these modes have been studied. It is demonstrated that for ω/ω1?0.66,1.33,1.66 and 2.33 coupled periodic motions exist brought forward by parametric excitation from the support point in addition to the resonances at ω/ω1?1.0 and ω/ω2?1.0 partly caused by the additive load term. |
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Keywords: | Non-linear dynamics Internal 2:1 resonance Combinatorial harmonic resonance Parametric instability |
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