# Vibration Control of Multi-Modular VLFS in Random Sea Based on Stiffness-Adjustable Connectors
## 4 Numerical Assessment on the Performance
### Performance of the Vibration Control Method
It is interesting to see that the controlled motions of all of the modules in a specific direction are at almost the same level, which implies that the control scheme realizes the equal weights assigned to the motions  
Figure 6: The amplitudes of the 1–in–1000 extreme responses of the (**a**) surge, (**b**) sway, (**c**) heave, (**d**) roll, (**e**) pitch, and (**f**) yaw motions for the wave incident angle of 0\({}^{\circ}\). of different modules. For the unintended suppression directions of the sway and roll motions shown in Figure 6b,d, the novel connectors with control significantly outperform the flexible connectors because of the couple between the different degrees of freedom. The performance of the vibration control method with the stiffness-adjustable connectors can be evaluated based on individual wave frequency. The results in Figure 6 come from the compound results calculated by Equation (26) and by the wave spectrum. Figure 7 only shows the intended motions of surge, heave, pitch, and yaw for the first module over the span of the wave frequency, based on Equation (26). For the surge motion, as shown in Figure 7a, the response of the novel connector is close to that of the hinged connector and is far smaller than that of the flexible connector. For the heave and pitch motions shown in Figure 7b,c, the novel connector (the blue curve) outperforms the other two connectors since the actuator of the novel connector can eliminate or reduce resonance near wave frequency of 0.628 rad/s and 0.9 rad/s by changing the connector stiffness. In the yaw response shown in Figure 7d, the rigid connector has lowest response because of its rigidity. The novel connector greatly reduces the peak of the flexible connector (red line) at 0.9 rad/s, but the novel connector (blue line) has a peak in the very low frequency below 0.25 rad/s. We can state that at low frequency, this peak at low is in fact very small and ignorable, in view of the quantity order of the yaw response. Note that the wave energy is mainly distributed at around 0.628 rad/s. The contribution of the responses from lower frequencies would be insignificant to the 1-in-1000 amplitude. Next, we present the scenario where the incident angle was 45\({}^{\circ}\). Figure 8a-d show the responses of the surge, heave, pitch, and yaw motions of the third module versus the wave frequency. In surge motion, the novel connector and rigid connector perform almost equally well and much better than the flexible connector. In the heave and pitch motions, the novel connector outperforms the other two connectors because the actuator of the novel connector takes effect. For the yaw motion, the novel connector performs better than the flexible connector around the main wave frequency of 0.628 rad/s but performs worse at very low frequencies. Since the peak of the yaw response is about 0.027 rad at low frequency, its contribution to the 1-in-1000 extreme responses is insignificant. Figure 8e-h show the 1-in-1000 extreme responses for the third module, which were induced by the wave spectrum in Equation (32). For the surge, heave, and pitch responses, the novel connector performs the best among the three types of connectors. As for the yaw motion, the novel connector greatly outperforms the flexible one. For a slender floating system, the hydrodynamic load on the floating structure is closely related to the wave incident  
Figure 7: The response amplitudes of the first module in the (**a**) surge, (**b**) heave, (**c**) pitch, and (**d**) yaw motions versus the wave frequency at the wave incident angle of 0\({}^{\circ}\). angle. It is necessary to study the effect of the wave incident angle on the performance of the novel connector. Next, the performance of the vibration control method was studied at different wave incident angles. To present the results neatly, we used the mean response of all of the modules at each degree of freedom to represent the essential nature of the system motion in that direction.