# Vibration Control of Multi-Modular VLFS in Random Sea Based on Stiffness-Adjustable Connectors
###### Abstract  
The response control of a very large floating structure (VLFS) is a crucial issue that affects the stability and safety of the structure. This paper presents a vibration control method for stabilizing the motion of a multi-modular VLFS by using a set of stiffness-adjustable connectors. The proposed connector consists of a cylindrical spring with an embedded actuator, making its stiffness adjustable. In a case study, a layout for such connectors is suggested to reduce the surge, heave, pitch, and yaw motions of the VLFS in random seas. To control the vibration responses of the VLFS, a mathematical model of the floating structure with the proposed connectors is established. A state feedback control scheme is developed using Sequential Quadratic Programming, which is able to adapt to varying wave conditions. Numerical studies indicate that the control method based on the stiffness-adjustable connectors was able to greatly reduce the responses of the modules when compared to flexible connectors and was also able to reduce the connector loads when compared to hinged connectors. Most importantly, this control method enables the elimination of resonant responses by changing the system stiffness. v 2022 2021 18 January 2022 2021 16 December 2021 18 January 2022 21 January 2022 21 February 2022 2  
Since the operation environment of VLFS is prone to changes and is rough, the vibration response of VLFS has become a key concern for its operational stability and security. To depress the response of VLFS, vibration control for VLFS has been considered. There are two fundamental approaches for vibration reduction: passive methods and active methods. Passive methods include employing breakwaters and anti-motion devices. Breakwaters, including bottom-founded breakwaters and floating breakwaters, are usually effective in reducing wave excitation on protected structures [11; 12; 13] in particular sea conditions but are poor at adapting to changing sea conditions. Some researchers have studied anti-motion devices that are attached to VLFS, such as plates [14], boxes [15] or oscillating water columns (OWC) [16], among others [17; 18; 19; 20; 21; 22]. All kinds of anti-motion devices can dissipate the wave energy and reduce the responses of a VLFS to a certain extent, but not as efficiently as active ones. In recent years, a semi-active control method [23] was proposed to reduce the vibration of a floating airport by intermittently tuning the stiffness of the connectors based on the amplitude death mechanism. This method can greatly reduce the vibration responses of a VLFS, but it may fail to perform in certain sea conditions. Active control methods are relatively complicated but can efficiently reduce the vibration of a VLFS in varying sea conditions. Pneumatic actuators combined with the PID algorithm have been used to decrease the heave motion of a VLFS [24]. Dynamic position (DP) [25; 26; 27] is a popular active method that can manipulate and alienate floating bodies into their designated positions by using a group of thrusts. The DP system is in fact a location positioning approach that does not take care of the vibration reduction of an individual floating body. In recent years, researchers attempted to decrease the responses of a VLFS using thrusts [28; 29], and encountered tremendous control output requirements, which make it difficult to implement this control method in real engineering practice. In this paper, a vibration control method is that uses a stiffness-adjustable connectors (briefly called novel connectors when at rest) is proposed for VLFS, which has the benefit of having relatively small output requirements. The novel connector consists of a cylindrical spring with an embedded actuator inside. The cylindrical spring is made of a high-strength polymer material with stiffness in three-translational directions. The actuator is hydraulically driven and is able to provide adaptive control forces to stabilize the floating system according to a control algorithm.