## 5 Response of FOWT-SFFC Driven by Environmental Loads
### Extreme Load Cases
Compared to LC2, the surge motion spectrum in LC3 also exhibit spectral peaks at \(f_{\text{pitch}}\) and the corresponding \(f_{\text{p}}\), but contains much more energy at low frequencies. This is because in LC3 the wind speed is much larger and the turbine has shut down, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Resposes** & **Variables** & **FOWT-SFFC** & **OC3 Hywind** & **OC4 DeepCwind** \\ \hline \multirow{8}{*}{Surge (m)} & Max & 8.7530 & 33.2500 & 14.4000 \\  & Min & 1.2890 & 9.2120 & 2.6090 \\  & Mean & 4.9662 & 20.2074 & 7.7644 \\  & Std & 1.1369 & 3.2095 & 1.4784 \\  & Skewness & 0.0896 & 0.07 & 0.0527 \\  & Kurtosis & 2.7689 & 2.9947 & 3.0070 \\ \hline \multirow{8}{*}{Heave (m)} & Max & 0.5586 & 0.8013 & 2.6480 \\  & Min & \(-\)0.6706 & \(-\)1.7200 & \(-\)2.3570 \\  & Mean & \(-\)0.0623 & \(-\)0.3708 & 0.0008 \\  & Std & 0.1374 & 0.3329 & 0.7258 \\  & Skewness & \(-\)0.0208 & \(-\)0.0088 & 0.0064 \\  & Kurtosis & 3.5578 & 2.8650 & 2.9258 \\ \hline \multirow{8}{*}{Pitch (deg)} & Max & 4.4120 & 8.1000 & 6.0420 \\  & Min & 0.0999 & 0.1925 & \(-\)0.3114 \\  & Mean & 2.2162 & 3.8556 & 2.5198 \\  & Std & 0.6191 & 1.0619 & 0.8608 \\  & Skewness & 0.0446 & 0.1357 & 0.1640 \\  & Kurtosis & 2.8594 & 2.9610 & 3.0697 \\ \hline \multirow{8}{*}{Stress (MPa)} & Max & 99.7660 & 153.7885 & 99.4315 \\  & Min & \(-\)13.8067 & \(-\)27.5297 & \(-\)0.6489 \\ \cline{1-1}  & Mean & 45.6250 & 53.5073 & 46.6412 \\ \cline{1-1}  & Std & 15.4343 & 23.5993 & 12.3898 \\ \cline{1-1}  & Skewness & 0.0036 & 0.0458 & 0.0606 \\ \cline{1-1}  & Kurtosis & 2.9151 & 2.9639 & 3.1234 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistics of foundation motions and tower base stress under LC3. while the assumed blade-pitch angles are all zeros, leading to maximum windward area of blades. Therefore, the wind thrust in LC3 is much larger than that in LC2. Considering also that the surge motion is heavily subjected to thrust, the appreciable energy of surge at low frequencies can thereby be manifested. For the heave motion in Figure 10b, the responses in LC2 and LC3 are peaked around both heave natural frequency (\(f_{\text{heave}}=0.0372\) Hz in Table 6) and corresponding \(f_{\text{P}}\). No response amplification occurs at low frequencies, in that the wind load can hardly affect the heave motion. At \(f_{\text{P}}\), the response energy in LC3 is remarkably higher than that in LC2, not only because the significant wave height Hs (Table 7) is 47.3% larger, but also because of the big difference in heave RAO (Figure 5). The reason why spectral peak at \(f_{\text{heave}}\) is much lower than that at \(f_{\text{P}}\) is due to the too small energy density at \(f_{\text{heave}}\). Meanwhile, it should be recognized that as the variances of heave (equal to area under power spectral curve minus square of mean) are small, the heave motions of FOWT-SFFC are actually less than 0.2 m in LC2 and 0.6 m in LC3 (Tables 9 and 10), evidencing the excellent motion of heave for FOWC-SFFC. As for pitch motion in Figure 10c, there are two peaks in the response spectrum of LC2, respectively around \(f_{\text{pitch}}=0.0342\) Hz and \(f_{\text{P}}\). But obviously more energy is concentrated around \(f_{\text{pitch}}\). This is due to the small damping of pitch (2.37% in Table 5) and much larger pitch RAO at T\({}_{\text{pitch}}\) than at T\({}_{\text{P}}\) (Figure 6). In LC3, as the moment induced by wind thrust has a significant effect on the pitch motion, the pitch response is pronounced at low frequencies. Figure 10: Response power spectra of foundation motions and tower base stresses of FOWT-SFFC under LC2 and LC3. **(a)** Surge motion spectrum; **(b)** heave motion spectrum; **(c)** pitch motion spectrum; **(d)** tower base stress spectrum. When it comes to tower base stress in Figure 10d, it is more complex. In LC2 and LC3, four peaks appear in the tower base stress spectrum. The first two peaks are at frequencies around \(f_{\rm pitch}\) and \(f_{\rm p}\).