# 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
The loads in the first and last groups are larger than those in the second and third groups, but the distribution of the load for the four groups is very similar. In comparison, the peak load of the novel connector is larger than that of the flexible connector by about 4.9%. This means that there is a cost to suppressing the multi-DOF motions by increasing the load of the novel connector. Figure 10i shows the contour map of the load of the hinged connector, and the peak load level is about \(8.99\times 10^{4}\) KN, which is much greater than that of the novel and  
Figure 9: The mean responses of a five–module floating structure in the (**a**) surge, (**b**) sway, (**c**) heave, (**d**) roll, (**e**) pitch, and (**f**) yaw motions for different wave incident angles. flexible connectors. Even worse, the high-level load appears to be in much broader area across the wave frequency and wave incident angle. The actuator output control force is calculated using Equation (17). These hot spots on the cloud map in Figure 10) appear in the domain spanned by the wave frequency and wave incident angle. The peak control force is up to the level of \(2.35\times 10^{4}\) KN, which is much smaller than the load level of the novel connector and the flexible connector. This means that with a small control force, the novel connector can achieve largely improved VLFS stability. Compared to the maximum control force of \(5\times 10^{4}\sim 7\times 10^{4}\) KN when using a full-control strategy [29] in the same VLFS, the control force of the novel connector is about \(1/2\) to \(2/3\) smaller in magnitude. Since the load difference between the novel connector and the flexible connector is smaller than the actuator peak load, the spring force of the flexible connector is larger than that of the novel connector when the actuator is switched on. Overall, we would like to comment that the control method with the novel stiffness-adjustable connector generally works well to suppress the intended surge, heave, pitch, and yaw motions with the connector layout shown in Figure 6. As for the roll and sway motions, there are no specific novel connectors arranged in the directions to control the motions. If additional novel connectors are deployed in these directions, the motions can  
Figure 10: The cloud charts of (**a–d**) the novel connector load of the first connector of all four groups (FC1–FC4), (**e–h**) the flexible connector load of the first connector of all four groups (NC1–NC4), (**i**) the hinged connector load (HC1) between the first and second module, and (**j**) the actuator output force of the first novel connector in the first group (NA1) in a domain spanned by the wave frequency and wave incident angle. be significantly reduced. Based on the stiffness-adjustable connectors, the vibration control method can apparently improve the stability of the floating structure even though the control forces expend little effort. The proposed method can also eliminate the resonances of the VLFS, making it more adaptive to various wave conditions.