# Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine
## 1 Introduction  
With the massive consumption of fossil fuels, energy and environmental pollution are becoming increasingly prominent problems. Developing clean renewable energy to replace the traditional fossil energy is a global urgent requirement. Under such a background, wind energy in deep-water area has attracted worldwide attention in recent years. Based on decades of experience from offshore oil and gas industry, several conceptual floating platforms have been proposed to support large wind turbines in deep-water regions, including spar, tension leg, barge, and semi-submersible. Different from fixed-bottom wind turbines, the associated rotation and translation of the floating platform induced by the wave and wind loadings can significantly augment the oscillation and loads of wind turbine. Therefore, vibration and load reduction of the floating offshore wind turbine (FOWT) is crucial to the life cycle safety. One approach for vibration alleviation is to utilize structural control devices, which has been successfully applied in civil engineering structures, such as buildings and bridges [1]. Moreover, because the passive vibration control is more robust and less expensive than the active vibration control, it has been extensively adopted in high-rise structures [2; 3] and offshore platforms [4; 5]. Thus, it is also expected to be a promising solution for inhibiting the vibration of FOWT. [PERSON] et al. [6; 7] established 3 degree-of-freedom (DOF) simplified structural models forbarge, spar and tension lag platform types of floating wind turbines, respectively, and optimized the tuned mass damper (TMD) configurations for each type of foundation using a genetic algorithm. They also concluded that the active control device achieved more load reductions than passive TMD. Compared with the other floating foundation, the barge-type floating wind turbines exhibit larger response [8]. Taking the ITI energy barge 5 MW FOWT as an example, [PERSON] et al. [9] pointed out that the maximum suppression rates of vibration responses vary from 20% to 50% as the mass ratio changes from 0.5% to 2%. Furthermore, [PERSON] et al. [10] investigated the active control strategies of TMD device and found that the wind turbine fatigue loads and generator error could be reduced effectively. With regard to the spar-type wind turbine, [PERSON] et al. [11,12] established a 5-DOF dynamic model for the Offshore Code Comparison Collaboration (OC3) Hywind spar-type wind turbine, and studied the effectiveness of TMD devices installed in nacelle and platform respectively. [PERSON] et al. [13] also investigated the effectiveness and feasibility of single and multiple TMD devices on a spar-type FOWT, and claimed that the spar TMD is more effective than the nacelle TMD. Apparently, TMD devices are effective in vibration and load mitigation for both barge-type and spar-type FOMTs. However, to the authors' knowledge, no studies have been reported to concern this issue of the semi-submersible foundation FOMTs. Nevertheless, currently, the semi-submersible foundation occupies the largest number of the few installed full-scale FOWT prototypes for its conspicuous capability in supporting the operational conditions of FOWT, such as the 2 MW WindFloat in the offshore of Portugal, and the 2 MW Mirai and 7 MW Shimpuu in the open sea of Japan. Although the structure system of the semi-submersible foundation is more complex than the other two types, it has the lowest pitch and roll motions, which is critical in the normal operation of wind turbines [14]. This study aims to investigate the potential application of optimized TMD in the semi-submersible FOWT. According to its particular characteristics, a customized 4-DOF dynamic model was derived based on the D'Alembert's principle. After identifying the unknown parameters, the simplified model was validated by the recognized FOWT analysis tool FAST [15]. To find the optimized configurations of TMD, both method of exhaustion and genetic algorithm were employed to avoid local minimum.