## 1 Introduction  
In engineering practice, the bluff body is a common non streamlined structure. When the fluid flow around the bluff body, alternating vortex shedding occurs on both sides of the back surface of the bluff body, which causes the bluff body to be subjected to periodic hydrodynamic forces. When the bluff body is elastically supported, the periodic fluid force will excite the vibration of the bluff body, and the vibration of the bluff body will change the vortex shedding mode of the bluff body [1]. This phenomenon of structural vibration caused by the interaction between fluid and structure is called flow-induced vibration (FIV) [2; 3]. A large number of practical engineering structures are bluff bodies, such as chimney towers, high-rise buildings, cooling towers, suspension bridges, offshore oil platforms, overhead cable lines, and submarine pipelines. FIV can cause fatigue damage to these buildings. Especially when the frequency of vortex shedding closes to the natural frequency of the bluff body, the vortex frequency will be locked-in. When lock-in occurs, the structure will be more seriously damaged by FIV, such as the collapse of Felibridge cooling tower caused by FIV. In many engineering and mechanical applications related to fluids, FIV is inevitably a major safety concern [4]. Therefore, research on the FIV of bluff bodies has great significance in theoretical research and practical applications. The FIV of a bluff body is a very complicated fluid-solid coupling process. Many studies have been done in this field, mainly focusing on the FIV characteristics and vibration control of the bluff body. The representative reviews of FIV of cylinders are by [PERSON] [5] and [PERSON] [6]. The control of FIV is embodied in two aspects. On the one hand, it is the suppression of vibration. [PERSON] [7] found that rectangular grooves on a cylinder can effectively control flow through PIV experiments. [PERSON] [8] used a water tunnel experimentation study and found that a synthetic jet can significantly change the scale of eddy current and wake mode. [PERSON] [9] discussed the flow around a corrugated cylinder by large eddy simulation and experiment, and they controlled the vibration of the tube bundle in a heat exchanger by adding a corrugated cylinder to the tube bundle array. [PERSON] [10] and [PERSON] [11] studied the inhibition effect of small control rods on vortex-induced vibration (VIV). The former compared the VIV characteristics under different rod numbers, diameter ratios and gap ratios. It was found that when the attachment had nine control rods, the diameter ratio was 0.15, and the clearance ratio was 0.6, the inhibition effect of VIV was the best. The latter simulated the VIV characteristics of a cylinder with three small control rods at different angles of attack and clearance ratios. It was found that the inhibition effect was the best when the angle of attack was 45 and the clearance ratio was 0.9. [PERSON] et al. [12] found a new method to control VIV: A twisted cylinder, which was applied to a semi-submersible offshore platform. Compared with a square cylinder, the amplitude of twisted cylinder decreased by 90% at the lock-in condition. On the other hand, [PERSON] et al. [13] studied the position and shape of the rough strip to control the VIV of the cylinder. It was found that the vibration could be effectively enhanced when the rough strip was located at 20\({}^{\circ}\), and it could be restrained when it was located at 120\({}^{\circ}\). At a highly reduced velocity, the rectangular and trapezoidal strips could promote the vibration, while the triangular and arc strips had little influence on the vibration. [PERSON] [14], [PERSON] [15; 16; 17; 18; 19] and [PERSON] [20] et al. adopted the control method of surface-attached straight strip roughness to study the energy conversion of the FIV of a cylinder.