A component mode synthesis algorithm for multibody dynamics of wind turbines

A system reduction scheme related to a multibody formulation of wind turbine dynamics is devised. Each substructure is described in its own frame of reference, which is moving freely in the vicinity of the moving substructure, in principle without any constraints to the rigid body part of the motion of the substructure. The system reduction is based on a component mode synthesis method, where the response of the internal degrees of freedom of the substructure is described as the quasi-static response induced by the boundary degrees of freedom via the constraint modes superimposed in combination to a dynamic component induced by inertial effects and internal loads. The latter component is modelled by a truncated modal expansion in fixed interface undamped eigenmodes. The selected modal vector base for the internal dynamics ensures that the boundary degrees of freedom account for the rigid-body dynamics of the substructure, and explicitly represent the coupling degrees of freedom at the interface to the adjacent substructures. The method has been demonstrated for a blade structure, which has been modelled as two substructures. Two modelling methods have been examined where the first is by use of fixed–fixed eigenmodes for the innermost substructure and fixed–free eigenmodes for the outermost substructure. The other approach is by use of fixed–free eigenmodes for both substructures. The fixed–fixed method shows good correspondence with the full FE model which is not the case for the fixed–free method due to incompatible displacements and rotations at the interface between the two substructures. Moreover, the results from the reduced model by use of constant constraint modes and constant fixed interface modes over a large operating area for the wind turbine blade are almost identical to the full FE model.