# 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
For example, the symbol \(\overline{x}=\frac{1}{N}\sum_{i=1}^{N}\mathbf{R}_{e}(x_{i})\) denotes the mean 1-in-1000 extreme surge responses of the whole floating structure in \(x\) direction. The mean responses of the five-module floating structure are presented in Figure 9, where the horizontal axis is the wave incident angle from \(0^{\circ}\) to \(90^{\circ}\). For the controlled motions of surge, heave, pitch, and yaw shown in Figure 9a,c,e,f, the control method by the novel connector (blue line) performs much better than that of the flexible connector. Especially in the surge, heave, and pitch motions, the result of the novel connector is close to that of the hinged connector due to its rigidity. By comparing the peak responses of the flexible connector, the novel connector can greatly reduce the surge by 91.2%, the heave by 88.8%, the pitch by 74.0%, and the yaw by 84.3%. These results indicate that the control method can effectively stabilize the modular floating structure and that it can greatly improve how stationary the system is. For those uncontrolled sway and roll responses, such as those illustrated in Figure 8b,d, the hinged connector performs better in general because of its rigidity feature. The novel stiffness-adjustable connector performs better than the flexible connector does because the interaction effects of the responses among the different degrees of freedom can be reduced when the actuators are activated. Figure 8: For the wave incident angle \(45^{\circ}\), the responses amplitudes of the first module in the (**a**) surge, (**b**) heave, (**c**) pitch, and (**d**) yaw responses versus the regular wave frequency and the amplitudes of 1–in–1000 extreme responses of the (**e**) surge, (**f**) heave, (**g**) pitch, and (**h**) yaw motions in random waves. The benefit of the vibration control method is also reflected in the dramatic reduction of connector loads when compared to the hinged connector. In this numerical simulation model, there are four groups of connectors to connect the five-module floating platform. The loads of the different connectors correspond to the frequency response in the domains of wave frequency and angle. The loads of the novel connector are calculated through Equation (12). For the flexible connector, the connector load is equal to the spring load and can be calculated through Equation (14). The load of the hinged connector is derived in article [32]. Basically, the load level among the different connector groups is the same. In a group, there are five connectors, among which the first four connectors are horizontally deployed in parallel, as indicated in Table 2. The load levels of the four connectors are the same, and the load level of the fifth connector is smaller than that of the first four. Figure 10 only illustrates the loads of the first connector in all of the connection groups. The variation in the load is investigated in a domain that is spanned by wave frequency and the wave incident angle. To make the presentation neat, only the load along \(x\) direction is presented here because the loads along other directions are much smaller. Figure 10a-d depict the loads of the novel connectors, which include the actuator force and the spring load. Although the direction of the actuator force may not always be identical to the direction of the spring load, in the worst case, the peak load of the novel connector is about \(3.63\times 10^{4}\) KN. The hot spots mainly appear at wave frequencies less than 0.3 rad/s. When comparing the four maps, the distribution and maximum values of the novel connector loads in four connector groups are almost the same. Figure 10e-h show the load distribution of the flexible connector, where the peak load is \(3.46\times 10^{4}\) KN. The peak load appears at the spot where the wave incident angle falls in the interval from \(45^{\circ}\) to \(70^{\circ}\), and the wave frequency is about 0.8 rad/s.