## 1 Introduction  
With the span of bridges increasing, the main girder of the bridge will become more flexible with lower stiffness and damping to resist the dynamic load. The wind load is the most common dynamic force acting on the long-span bridge in the natural environment [1, 2]. Airflow flows across the bridge girder and yields the alternating vortex shedding in the wake. When the vortex shedding frequency is closed or equaled to that of the structure, the structure has the potential for the resonance phenomenon to occur, i.e., vortex-induced vibration (VIV). The VIV is the primary issue that is caused by airflow in bridge engineering because it occurs at a low velocity (e.g., the VIV of the Great Belt East Bridge was observed at an incoming flow velocity of 4-12 m/s as presented by [PERSON] et al. [1] and leads to structural fatigue when undergoing frequent vibration [3, 4]. Therefore, it is necessary to present an efficient control scheme to suppress the amplitude of VIV [4, 5, 6]. The external shape of the bluff body can influence the performance of the VIV [8]. If the target structure is streamlined, the flow separation cannot occur and the alternating vortex shedding cannot form; it is hard for the VIV to appear in those structures. Therefore, the box girder of the bridge is designed as near streamline for alleviating the VIV. Due to the box girder being not entirely streamlined, the VIV often happens when the airflow velocity attains a specific value, i.e., the wake vortex frequency is equal to that of the box girder at this velocity [2; 9]. In addition, the affiliate parts (i.e., railing, maintenance track, and streetlamps) that are set in the box girder also can affect the characteristics of the main girder and the fluctuation of the aerodynamic force. [PERSON] et al. [10] changed the straight railing along the span-wise direction to the wave railing for forming the three-dimensional disturbance to mitigate the VIV of a long-span bridge. The results indicated that when the wave length of the wavy bar was set as 0.5 or 1 times of the bridge girder height, the vertical and torsional VIV amplitudes were entirely suppressed and both sides of the upper surface were the best installation locations. However, this form of wave railing will occupy more space, impacting usability. The size and location of the horizontal bar of the railing had a dramatic influence on the flow structure of the position near the leading edge and the torsional VIV responses of the main girder as presented by [PERSON] et al. [11]. Moreover, [PERSON] et al. [12] studied the effect of the inclination angle of the railing on the VIV of the bridge girder. For suppressing the VIV, the control effectiveness of the inclined railing was superior to the railing with the inclination angle of zero. In addition to using non-structural parts to suppress the wind-induced vibration, many other control strategies, such as the structural and aerodynamic measures, have been presented in recent years [7; 13; 14; 15]. [PERSON] et al. [7] designed tuned mass dampers (TMDs) to mitigate the vibration amplitude of the Great Belt East bridge. The results found that the VIV response of the bridge girder with TMDs was at the allowed range using a time-domain simulation. [PERSON] and [PERSON] [13] applied the TMDs in the Rio-Niteroi Bridge to alleviate the VIV amplitude. They discovered that subsidiary active or tuned vibration absorbers had a remarkable influence on attenuating the dynamic responses on the main girder. [PERSON] et al. [16] studied the parameter determination of the tuned mass damper in alleviating the VIV of the bridge girder. They found that the equivalent damping ratio (EDR) is only determined by the TMD parameters, not the aerodynamic parameters. Moreover, the EDR is closely related to the uncertainty in the stiffness of the bridge according to the result of the uncertainty analysis. The underlying control mechanism of TMD is that changing the vibrational frequency and the structural damping mismatch the frequency of the aerodynamic force.