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 ωω. Assuming that the fundamental blade and edgewise eigenfrequencies have the ratio of ω2/ω1≃2ω2/ω1≃2, internal resonances between these modes have been studied. It is demonstrated that for ω/ω1≃0.66,1.33,1.66ω/ω1≃0.66,1.33,1.66 and 2.332.33 coupled periodic motions exist brought forward by parametric excitation from the support point in addition to the resonances at ω/ω1≃1.0ω/ω1≃1.0 and ω/ω2≃1.0ω/ω2≃1.0 partly caused by the additive load term.