## 1 Introduction  
Long-span bridges are usually adopted to allow people to cross rivers or straits, and have been widely built throughout the whole world. In particular, a considerable amount of large-span bridges (i.e., suspension bridges and cable-stayed bridges) have been constructed or are under construction in China, with the rapid development of the economy in the last three decades. However, with an increase in span, long-span bridges become more flexible and more prone to vibrating under unsteady wind loads. Although the cross-section of a single box girder is generally designed to be similar to a streamline, the alternating vortex shedding from the upper and lower surfaces of the girder cannot be completely eliminated and will probably result in vortex-induced vibrations (VIVs) [1]. There can be different behaviors of frequent VIVs in long-span bridges because of differences in the cross-sections of the main girders [2; 3; 4]. However, unsteady vortex shedding from the girders should be mainly responsible for the occurrence of VIVs. [PERSON] et al. [5] performed a field investigation on the VIV of the Great Belt East Bridge (Storebeit Suspension Bridge) in Denmark. This bridge was often observed to vibrate in low wind speeds of 4-12 m/s, with the single mode vibrations of a relatively large amplitude excited by vortex shedding. [PERSON] and [PERSON] [6] observed a significant vibration due to vortex shedding on the Trans-Tokyo Bay Crossing Bridge. The first-mode VIV with a maximum amplitude exceeding 50 cm peaked at the wind speed of 16-17 m/s. [PERSON] et al. [7] conducted a field measurement on the Xihoumen Suspension Bridge, which is the longest suspension bridge in China. The investigation results indicated that the VIV occurred more frequently at a low wind speed range of 6-10 m/s, with the wind direction being nearly perpendicular to the bridge axial line. As mentioned in the above three bridges, the VIVs of these long-span bridges occurred at wind speeds of 4-17 m/s, which was a frequent in-situ wind speed range at these bridges. It could be concluded that the VIVs will frequently appear at low speeds if there are no control measures implemented on these bridges. Two kinds of control strategies (i.e., active and passive control methods) have been developed to mitigate the wind-induced vibrations of long-span bridges. [PERSON] et al. [8] designed tuned mass dampers (TMDs) to control the potential wind-induced vibrations of the Great Belt East Bridge. The time-domain simulation results indicated that the girder and TMD responses did not exceed the maximum allowable values. The TMDs were then applied to control the VIVs of the Rio-Niteroi Bridge in Rio de Janeiro, Brazil [9; 10]. The numerical simulation results showed that the TMDs under active control had a better performance in reducing and controlling the responses of the VIVs. [PERSON] et al. [11] employed an active span-wise suction method to control the vortex shedding from the test models of the Great Belt East Bridge. The alternative approach was the passive aerodynamic method, which employed accessory components on the bridges, such as guide vanes [5] and wing plates [12; 13] to improve aerodynamic performance. It was found that the guide vanes were effective in suppressing vortex-induced vertical oscillations of the suspension bridge of the Great Belt Bridge, as reported in [PERSON] et al. [5]. In addition, the airflow around the main girder could be modified by attaching or adjusting some non-structural parts (such as railings, parapets, maintenance rails and collision barriers) with specific shapes at the specific positions of the main girder [14; 15]. [PERSON] et al. [16] used the span-wise sinusoidal perturbation method (SPPM) module in both the leading and trailing edges of the plate girder bridge. The experimental results indicated that VIV responses could be dramatically suppressed with higher wave steepness. Based on the research findings by [PERSON] and [PERSON] [17] and [PERSON] et al.