Multibody dynamics of floating wind turbines with large-amplitude motion

• Conservation of momentum is directly applied to entire multibody system.
• Only six EOMs are needed for mechanically connected rigid-body system.
• Nonlinear large-amplitude motions of floating wind turbines are investigated.
• Decoupled translational and rotational accelerations facilitate numerical solution.

A new approach to multibody dynamics is investigated by treating floating wind turbines as multibody systems. The system is considered as three rigid bodies: the tower, nacelle and rotor. Three large-amplitude rotational degrees of freedom (DOFs) of the tower are described by 1-2-3 sequence Euler angles. Translation of the entire system is described by Newton’s second Law applied to the center of mass (CM) of the system and transferred to 3 translational DOFs of the tower. Additionally, two prescribed DOFs governed by mechanical control, nacelle yaw and rotor spin, are combined with the 6 DOFs of the tower to formulate the 8-DOF equations of motion (EOMs) of the system. The CM of the system is generally time-varying and not constrained to any rigid body due to the arbitrary location of the CM of each body and relative mechanical motions among the bodies. The location of the CM being independent of any body is considered in both the solution to 3 translational DOFs and the calculation of angular momentum of each body for 3 rotational DOFs. The theorem of conservation of momentum is applied to the entire multibody system directly to solve 6 unknown DOFs. Motions computed using the six nonlinear EOMs are transformed to each body in a global coordinate system at every time-step for use in the computation of hydrodynamics, aerodynamics and restoring forcing, which preserves the nonlinearity between external excitation and structural dynamics. The new method is demonstrated by simulation of the motion of a highly compliant floating wind turbine. Results are verified by critical comparison with those of the popular wind turbine dynamics software FAST.