This paper investigates the use of single and multiple tuned mass dampers (TMDs) for passive control of edgewise vibrations of nacelle/tower and spar of spar‐type floating wind turbines (S‐FOWTs). Uncontrolled and controlled mathematical models of the S‐FOWT are developed by using Euler‐Lagrangian energy formulations. In these models, the aerodynamic properties of the blade, variable mass and stiffness, gravity, the interactions among the blades, nacelle, spar and mooring system, the hydrodynamic effects, the restoring moment, and the buoyancy force are considered. The vibrations of the blades, nacelle, tower, and spar are coupled in all degrees of freedom and in all inertial, dissipative, and elastic components. In the controlled model, several set of horizontal TMDs are placed in the spar at various depths and the coupling of these TMDs with the nacelle and spar motions is considered. The control effectiveness is evaluated by the reduction of the root‐mean‐square and maximum response. The control feasibility is examined by using the spar sinking and the TMD maximum strokes. The investigations using nonlinear time–domain simulation show that a single TMD can reduce up to 40% of the nacelle sway displacement and the spar roll, and that the reduction observed with multiple TMDs is 50%. The influence of the spar TMD is more significant than that of the nacelle TMD. The spar TMDs are less effective when their positions are lower. In all the cases studied, good heave performance of the S‐FOWT is maintained. Copyright © 2014 John Wiley & Sons, Ltd.

Semi-active control of vibrations of spar type floating offshore wind turbines floating offshore wind turbine;spar-type;edgewise vibration;tuned mass damper;semi-active control; 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.