# Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine
## 4 Performance Verification and Analysis of the Optimized TMDs
On the other side, the natural frequency of turbine tower is much higher and its oscillations are mostly excited by the wide-band wind spectrum. As can be seen in Table 7, almost all the reduction ratios of high stiffness TMD is larger than the low stiffness TMD, regardless of whether considering the extreme or fatigue index or not. Furthermore, lower stiffness of TMD will frequently collide on the stop walls, which may increase the cost of maintenance. Therefore, the low stiffness TMD is not recommended for FOWTs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Evaluation Index**} & \multicolumn{3}{c}{**Low Stiffness TMD Mass (kg)**} & \multicolumn{3}{c}{**High Stiffness TMD Mass (kg)**} \\ \cline{3-8}  & & **8000** & **10,000** & **20,000** & **8000** & **10,000** & **20,000** \\ \hline \multirow{8}{*}{10 m/s} & 95 th Pitch & \(-0.88\%\) & \(-1.25\%\) & \(-2.88\%\) & \(-0.37\%\) & \(-0.59\%\) & \(-1.55\%\) \\  & 95 th Roll & \(-0.45\%\) & \(-0.68\%\) & \(-1.17\%\) & \(-0.50\%\) & \(-0.64\%\) & \(-0.92\%\) \\  & 95 th fore-aft \(T_{\text{TB}}\) & \(-1.04\%\) & \(-1.30\%\) & \(-2.71\%\) & \(-0.83\%\) & \(-1.06\%\) & \(-2.00\%\) \\  & DEL of side-side \(T_{\text{TB}}\) & 24.09\% & 29.20\% & 37.86\% & 29.84\% & 32.78\% & 39.32\% \\  & DEL of fore-aft \(T_{\text{TB}}\) & 1.54\% & 1.48\% & 2.39\% & 2.51\% & 3.77\% & 7.78\% \\ \hline \multirow{8}{*}{18 m/s} & 95 th Pitch & \(-0.81\%\) & \(-0.89\%\) & \(-0.57\%\) & \(-0.60\%\) & \(-0.75\%\) & \(-1.41\%\) \\  & 95 th Roll & 0.12\% & 0.02\% & \(-1.17\%\) & 0.36\% & 0.33\% & \(-0.52\%\) \\ \cline{1-1}  & 95 th fore-aft \(T_{\text{TB}}\) & \(-1.25\%\) & \(-1.51\%\) & \(-3.18\%\) & \(-0.48\%\) & \(-0.54\%\) & \(-1.71\%\) \\ \cline{1-1}  & DEL of side-side \(T_{\text{TB}}\) & 4.25\% & 6.79\% & 18.50\% & 1.16\% & 3.08\% & 15.32\% \\ \cline{1-1}  & DEL of fore-aft \(T_{\text{TB}}\) & \(-1.26\%\) & \(-1.40\%\) & \(-3.62\%\) & 1.58\% & 1.43\% & 0.18\% \\ \hline \multirow{8}{*}{37 m/s} & 95 th Pitch & 0.04\% & 0.09\% & 0.70\% & 0.24\% & 0.39\% & 0.63\% \\  & 95 th Roll & \(-0.41\%\) & \(-0.57\%\) & \(-1.05\%\) & \(-0.41\%\) & \(-0.55\%\) & \(-1.04\%\) \\ \cline{1-1}  & 95 th fore-aft \(T_{\text{TB}}\) & 0.12\% & 0.99\% & 1.60\% & \(-1.05\%\) & \(-1.46\%\) & \(-2.97\%\) \\ \cline{1-1}  & DEL of side-side \(T_{\text{TB}}\) & \(-1.82\%\) & \(-1.80\%\) & \(-2.27\%\) & \(-1.39\%\) & \(-1.48\%\) & \(-1.67\%\) \\ \cline{1-1}  & DEL of fore-aft \(T_{\text{TB}}\) & \(-1.40\%\) & \(-1.90\%\) & \(-4.62\%\) & \(-0.23\%\) & \(-0.55\%\) & \(-1.97\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Response reduction ratios of multiple TMD devices. Figure 7: Time-history samples of environmental load conditions: (**a**) wind velocity; and (**b**) wave height. With regard to the platform pitch and roll motion, the controlling performance of TMD is negative for most cases. The absolute values of reduction ratio are relatively small and increasing with the increment of TMD mass. This phenomenon can be explained by the mass ratio and location of TMD. Firstly, the mass ratio of TMD (20,000 kg) to the whole system is 0.14% which is significantly small than the empirical value in building structure control. However, the mass ratio of TMD (20,000 kg) to the 5 MW turbine is 3.33%. Thus, it is not surprising that the TMD devices in this work have negligible effects on the platform motion. Secondly, as the turbine inclines, the gravity of TMD device installed in the nacelle will deteriorate the system tilt. The DEL of tower base moment \(T_{\text{TB}}\) in the fore-aft and side-side directions represents the fatigue loads. Under the two operating conditions (10 m/s and 180 m/s), TMD is capable of mitigating the DELs substantially. With the increase of TMD mass, the control effects also improved gradually. Compared with side-side, the reduction ratio of fore-aft direction is lower. Nevertheless, the absolute moments in the fore-aft direction are several times larger than the side-side.