## 4 Results
### Hydrodynamic Response
#### 4.1.3 Dynamic Response  
The modal analysis was performed, and the natural frequencies of the first 20 natural modes are listed in Table 4. The comparison of the natural frequencies of the SFT supported by different mooring cable configurations gives a direct measure of the cable system stiffness. The natural frequencies of the SFT increase when the cable configuration is changed from C1 to C3. Configuration C3 provides more stiffness to the SFT than configurations C1 and C2, and similarly, configuration C2 provides more than configuration C1. However, the natural frequencies of the SFT for the three mooring cable configurations are very close to each other for higher modes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Mode** & **C1** & **C2** & **C3** & **Mode** & **C1** & **C2** & **C3** \\ \hline
1 & 0.5660 & 0.6997 & 0.824 & 11 & 14.0467 & 14.0359 & 14.0408 \\
2 & 1.2825 & 1.1542 & 1.2144 & 12 & 20.0309 & 20.0309 & 20.0309 \\
3 & 2.2606 & 2.2606 & 2.2606 & 13 & 20.0417 & 20.0417 & 20.0417 \\
4 & 2.5041 & 2.5041 & 2.5041 & 14 & 26.2123 & 26.2123 & 26.2123 \\
5 & 5.0739 & 5.0907 & 5.1103 & 15 & 27.0944 & 27.0975 & 27.1010 \\
6 & 5.1324 & 5.1025 & 5.1160 & 16 & 27.1051 & 27.0996 & 27.1021 \\
7 & 8.7454 & 8.7454 & 8.7454 & 17 & 35.1364 & 35.1364 & 35.1364 \\
8 & 8.9895 & 8.9895 & 8.9895 & 18 & 35.1522 & 35.1522 & 35.1522 \\
9 & 9.0143 & 9.0143 & 9.0143 & 19 & 43.6074 & 43.6074 & 43.6074 \\
10 & 13.985 & 13.991 & 13.998 & 20 & 44.1137 & 44.1155 & 44.1176 \\ \hline \end{tabular}
\end{table} 
Table 4: Modal analysis of the SFT and comparison of the first 20 natural frequencies (Hz) for each cable configuration. Figure 5: Comparison of static displacement and internal force envelope curves of the SFT for three mooring configurations: (**a**) vertical and transverse rotation; (**b**) vertical and transverse displacement; (**c**) vertical and transverse bending moment; and (**d**) vertical and transverse shear force. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**A**} & \multicolumn{3}{c}{**B**} & \multicolumn{3}{c}{**C**} \\ \cline{2-10}  & **C1** & **C2** & **C3** & **C1** & **C2** & **C3** & **C1** & **C2** & **C3** \\ \hline \(\theta_{\mathrm{Y}}\) (\(\times 10^{-3}\) rad) & \(-0.441\) & \(-0.585\) & \(-0.512\) & \(0.022\) & \(0.027\) & \(0.024\) & \(0.452\) & \(0.599\) & \(0.524\) \\ \(\theta_{\mathrm{Z}}\) (\(\times 10^{-3}\) rad) & \(0.312\) & \(0.196\) &Figure 6 represents the comparison of the hydrodynamic response of the SFT at Section A, using three mooring cable configurations. Figure 6a shows the comparison of the SFT displacements in the transverse direction: configuration C1 has the largest displacement, followed by configuration C2, and configuration C3 has the minimum displacement. The maximum displacements of the SFT for configuration C1, C2 and C3 are 0.046 m, 0.021 m and 0.011 m, respectively. The same trend occurs for the transverse bending moment (M\({}_{\mathrm{z}}\)), as shown in Figure 6b. The maximum bending moments of SFT for configurations C1, C2 and C3 are 25,066.628 kN-m, 11,943.442 kN-m and 6838.661 kN-m, respectively. Figure 6c shows the comparison of the SFT displacement in the vertical direction; configuration C2 has the largest displacement, followed by configuration C3, and configuration C1 has the minimum displacement. The maximum displacements of SFT for configurations C1, C2 and C3 are 0.029 m, 0.035 m and 0.032 m, respectively. The same trend occurs for the vertical bending moment (M\({}_{\mathrm{Y}}\)), as shown in Figure 6d. The maximum bending moments of SFT for configurations C1, C2 and C3 are 12,202.859 kN-m, 13,694.792 kN-m and 12,934.200 kN-m, respectively. Figure 7 represents the comparison of the hydrodynamic response of SFT at Section B. Figure 7 shows the same trend as described to that of Section A. However, the general response at Section B is larger than that of Section A.