Hybrid State-Space Time Integration of Rotating Beams

Modeling and efficien design of wind turbines require efficien and accurate computational methods for dynamic analysis of the different components. In the present paper an efficien hybrid formulation for beams in a rotating frame of reference is presented for analysis of the rotor system. It is demonstrated that the equations of motion take a particularly simple form when starting from a hybrid state-space in terms of local displacements relative to the rotating frame and absolute velocities using similar interpolation. The equations of motion are formulated for small finit deformation beam elements in terms of translational as well as rotational degrees of freedom and include the effect of geometric stiffness. The dynamic equations are derived from Lagrange’s equation and combined with a kinematic relation into a convenient hybrid state-space format.