Vibration control for a semi-submersible floating offshore wind turbine with optimal ultra-low frequency electromagnetic tuned inerter-mass dampers

The platform of a semi-submersible floating offshore wind turbine is prone to large ultra-low frequency pitch motion in a complex marine environment. To address this problem, this study proposes the application of multiple ultra-low frequency electromagnetic tuned inerter-mass dampers (UF-ETIMDs) inside the offset columns to mitigate the pitch motion of the platform. An UF-ETIMD is achieved by replacing the viscous damping of the classical tuned mass damper (TMD) with an electromagnetic inerter damper in series with a tuning spring, which will tune the inerter's resonant frequency. A constant-force spring is added in parallel with the main spring to neutralize the gravity force of the mass damper that can effectively reduce static elongation of the main spring while tuning the resonant frequency of the mass to ultra-low frequency of the pitch motion. Thus UF-ETIMDs can achieve a double-tuned electromagnetic damping system to enhance the vibration mitigation performance of the platform. The parametric optimization of the UF-ETIMDs is conducted based on the H∞ optimization criteria, whose target is to minimize the peak value of platform pitch in the frequency domain. To analyze the performance of the UF-ETIMD on the semi-submersible FOWT, a 20-degree-of-freedom (DOF) analytical model has been developed for the semi-submersible FOWT coupled with three UF-ETIMDs, retrofittable inside the platform. The performance of the UF-ETIMDs is examined and compared with the classical TMDs under different combinations of wind and wave loadings and in both operational and parked conditions. Results found that UF-ETIMDs can achieve a better performance than TMDs in mitigating the platform pitch of the semi-submersible FOWT. The potential powers in the UF-ETIMDs system that could be converted from vibrations to usable electricity are also examined.