Non-linear dynamics of wind turbine wings

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 omega. Assuming that the fundamental blade and edgewise eigenfrequencies have the ratio of omega(2)/omega(1) similar or equal to 2, internal resonances between these modes have been studied. It is demonstrated that for omega/omega(1) similar or equal to 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 omega/omega(1) similar or equal to 1.0 and omega/omega(2) similar or equal to 1.0 partly caused by the additive load term. (C) 2006 Elsevier Ltd. All rights reserved.