# Vibration Control of Multi-Modular VLFS in Random Sea Based on Stiffness-Adjustable Connectors
## 5 Conclusions  
In this paper, we proposed a novel stiffness-adjustable connector and a related vibration control method for multi-modular VLFS. The novel connector is composed of an annular spring to provide basic flexibility and an embedded hydraulic actuator to provide control force. The benefit of using the novel connector can greatly reduce the control forces, making its application possible. These individual connectors can be combined into a desirable connection layout to suppress all types of movement experienced by a modularized VLFS in random sea conditions. In the study, a connector layout to suppress suppressing the surge, heave, pitch, and yaw motions of a five-module floating structure is suggested. To estimate the performance of the vibration control method, a mathematical model is developed that is associated with a state-feedback control scheme. The feedback gains are obtained by using Sequential Quadratic Programming. In the numerical studies, we verified the vibration control method in the different wave frequencies and wave incident angles and compared the performance of the stiffness-adjustable connector with flexible connectors and hinged connectors. The results show that the control method can greatly reduce the responses of the VLFS in random sea conditions while using small control forces. In the connector load, the peak load of the novel connector is slightly larger than that of the flexible connector but much smaller than that of the hinged connector. More importantly, the vibration control method enables the modular floating system get rid of resonant responses to random sea conditions, adaptive to the changes in wave conditions.  
In this study, the modules are treated as rigid bodies so that the case study remains linear to the motion equation. The nonlinearity is not considered, which could be caused by a large deflection in the flexible modules or mooring systems. The loads of the novel connector could be estimated in both extreme responses and non-extreme responses, and the loads of non-extreme states could be used for fatigue-driven design [40]. The resonant response of floating structures is strongly influenced by non-radiative damping, which is usually represented by empirically calibrated linear damping, which fits the approach of this study. The frequency domain approach is unsuitable for dealing with transient responses. For transient and nonlinear responses, the implementation of a time-domain-adaptive control strategy would be required. The connector model was studied in a long-and-slender VLFS with multiple modules with a simple 2D structure. In fact, there are no technical barriers for the potential application of these connectors to in complicated topological VLFS with three dimensions, which could be of great interest for future studies.  
Conceptualization, S.X. and D.X.; methodology, D.X.; software, S.X.; validation, S.X. and D.X.; resources, H.Z.; data curation, W.Y.; writing--original draft preparation, S.X.; writing--review and editing, D.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 11902084.  
Not applicable.  
The authors declare no conflict of interest.