## 1 Introduction
It was found that the vibration of the cylinder with roughness strips was greatly enhanced under the condition of flow reduced velocity, and the kinetic energy of the fluid was more converted into the mechanical energy of vibration. In addition, with the rapid development of aerospace engineering, ocean engineering and wind engineering, more and more scholars begin to pay attention to the flow around multi-cylinders and FIV. [PERSON] [21] studied the vibration response of tandem cylinders in the direction of flow through a wind tunnel, one of which was fixed. The influence of the spacing ratio on vibration was analysed, and the wake structure of the cylinder was observed by the smoke visualization method. [PERSON] [22] researched the interaction between wakes of several parallel cylinders in turbulent flow. It was found that the Prandtl number, heat flux and vortex structure were affected by wake interaction and clearance flow deflection. [PERSON] [23] developed a new solver to calculate the flow around multiple cylinders. The results show that the flow was greatly influenced by the Reynolds number and the spacing ratio. With the increase of the Reynolds number, the vortex shedding speed was faster, and the frequency of parallel three cylinders was larger than that of three cylinders in tandem. [PERSON] et al. [24] studied the response and galloping of three tandem cylinders by numerical simulation. It was found that when the spacing ratio was small, the large-amplitude vibration of the cylinders was mainly affected by the wake-cylinder. While at the larger spacing ratio, the vibration response of the upstream cylinder was similar to that of an isolated single cylinder and was no longer affected by the downstream cylinder. [PERSON] et al. [25] studied the FIV and energy recovery of three tandem cylinders with rough strips, and they found that the maximum amplitude of the upstream cylinder could reach 2.8 \(D\). The total power increased with the increasing of the reduced velocity of the water, and the power peaked at roughly 85.26 W. For the case of multiple cylinders, the flow field condition and the vibration of the cylinder were more complicated than the vibration of the single cylinder. The two cylinders are one of the simplest multi-cylinder forms and have been the basis for multi-cylinder research. [PERSON] et al. [26] collated and analysed the results of previous studies on the flow around two cylinders, and they found that the forces acting on the cylinder and the wake structure were influenced by many factors, such as the distance between the cylinders, the Reynolds number, the arrangement of the cylinders, and the size of the cylinder. [PERSON] et al. [27] studied the VIV of the two tandem cylinders. It was found that the maximum amplitude of the downstream cylinder of the two tandem cylinders was significantly larger than that of the single cylinder, and the critical buckling deceleration was between 5.0 and 6.0 at different spacing ratios. [PERSON] et al. [28] simulated the FIV characteristics of a circular cylinder and a square cylinder arranged in tandem. The results were contrary to those of two cylinders in series. The square cylinder installed downstream showed a VIV-type response at different spacing ratios without galloping. [PERSON] et al. [29] simulated the vibration of two cylinders with different diameters. It was found that the vortex shedding modes were different under different arrangement modes, and only the vibration of staggered arrangement was periodic and stable. [PERSON] et al. [30] numerically simulated the FIV response of two staggered cylinders and classified the relationship between gap distance, reduced velocity and vibration response, which were divided into a low reduced velocity zone, a critical state zone, a wake dominant zone, a gap flow dominant zone, and so on. [PERSON] et al. [31] studied the VIV of two tandem cylinders in the wake-dominant region.