A semi-active algorithm for edgewise vibration control of the spar-type floating offshore wind turbine (SFOWT) blades, nacelle and spar platform is developed in this paper. A tuned mass damper (TMD) is placed in each blade, in the nacelle and on the spar to control the vibrations for these components. A Short Time Fourier Transform algorithm is used for semi-active control of the TMDs. The mathematical formulation of the integrated SFOWT-TMDs system is derived by using Euler-Lagrangian equations. The theoretical model derived is a time-varying system considering the aerodynamic properties of the blade, variable mass and stiffness per unit length, gravity, the interactions among the blades, nacelle, spar, mooring system and the TMDs, the hydrodynamic effects, the restoring moment and the buoyancy force. The aerodynamic loads on the nacelle and the spar due to their coupling with the blades are also considered. The effectiveness of the semi-active TMDs is investigated in the numerical examples where the mooring cable tension, rotor speed and the blade stiffness are varying over time. Except for excessively large strokes of the nacelle TMD, the semi-active algorithm is considerably more effective than the passive one in all cases and its effectiveness is restricted by the low-frequency nature of the nacelle and the spar responses.
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