## 4 Simulation and Discussions  
### Load Response Analysis of Connectors  
Because connectors \(C_{1}\) and \(C_{2}\) were symmetrically arranged, only the calculation results of connector \(C_{1}\) are given (Figure 10), where the RAO under different directions is shown.  
Generally speaking, the wave load on the connector reaches its maximum at low frequencies, particularly near the wave direction of 75 degrees. Furthermore, the maximum value of the three-direction load decreases in the order of \(Fx\), \(Fz\) and \(Fy\). Therefore, special attention should be paid to the strength of the axial and vertical directions when designing the connector. Specifically, the axial force of the connector showed a clear increase as the wave direction increased, and the maximum value was 1.36 \(\times\) 10\({}^{7}\) N at 75 degrees (Figure 10a).  
Figure 10: Shear force under different wave directions. (**a**) Shear force along the \(x\) axis; (**b**) Shear force along the \(y\) axis; (**c**) Shear force along the \(z\) axis.  
Figure 9: Relative error.  
When the wave direction was small, the horizontal shear force was small, which can be ignored when compared with the maximum value (1.63 \(\times\) 10\({}^{6}\) N) under 60\({}^{\circ}\) (Figure 10b). The vertical shear force distribution exhibited little change with changes in the wave direction, and the maximum value appeared at 75\({}^{\circ}\), which was 1.28 \(\times\) 10\({}^{7}\) N (see Figure 10c).  
In terms of high-frequency loads, almost no obvious wave-induced vibration phenomenon was observed within the calculation frequency range for the load along the \(y\) axis, whereas the first-order resonance frequency of the load along the \(x\) axis was around 3.5 rad/s. In addition, the first-order resonance frequency along the \(z\) axis was between 1.5 rad/s and 2.0 rad/s, which was close to the natural wave frequency range. Therefore, more attention should be paid to the wave-induced vibration phenomenon of the connector in subsequent checks of connector strength in the \(z\) direction.  
In order to study the influence of modes on the connector, the load of the first three modes with the greatest influence on the connector load under 75 degrees were taken, as shown in Figure 11. It can be seen from Figure 11a that the load of the connector in the \(x\) direction was mainly determined by the two-node horizontal bending mode. Furthermore, it can be seen from Table 2 that the natural frequency of two-node horizontal bending was 3.64 rad/s (0.58 Hz), which is consistent with the peak frequency of the first-order resonance spectrum in Figure 10a.  
As for the \(y\) direction load of the connector, it can be seen from Figure 11b that the three-node torsion and horizontal bending mode have a great influence on shear force in the \(y\) direction, but this is mainly determined by the three-node torsion mode. Furthermore, the two-node torsion mode has little contribution to the \(y\) direction load. Compared with Figure 4b, it can be seen that the lateral relative displacement of the two-node torsion at the connector was small, resulting in less force. As for the \(z\) direction load, it can be seen from  
Figure 11: The contribution of different modes to loads. (**a**) The contribution of different modes to \(Fx\); (**b**) The contribution of different modes to \(Fy\); (**c**) The contribution of different modes to \(Fy\).  
Figure 11c that it was mainly determined by the first-order torsion mode at low frequencies and the three-node vertical bending mode at medium-high frequencies.