## 5 Conclusions  
Through wind tunnel static and free vibration tests, the effects of the Reynolds number on the aerodynamic forces and VIV response of a streamlined box girder were studied. The underlying mechanism of the Reynolds number effect on VIV was revealed in conjunction with the time-frequency characteristics of the vibration. The conclusions are as follows.  
(1) As the Reynolds number increases from 10\({}^{4}\) to 1.2 \(\times\) 10\({}^{5}\), the static drag coefficient of the streamlined box girder significantly decreases, the lift coefficient slightly increases, and the pitching moment coefficient remains almost unchanged. The mean values of the wind pressure coefficients on the main beam surface exhibit a weak Reynolds number effect in certain regions, primarily in the upper surface area from \(D_{\rm d}\) = 0.07 to 0.33, and at the locations of two maintenance vehicle tracks on the lower surface (\(D_{\rm d}\) = 0.22 and 0.79). The RMS values of the wind pressure coefficients show a significant Reynolds number effect. Overall, both the upper and lower surface RMS values decrease as the Reynolds number increases.  
(2) The VIV of the main beam has a significant effect on the Reynolds number. As the Reynolds number increases from 3.2 \(\times\) 10\({}^{4}\) to 8.3 \(\times\) 10\({}^{4}\), the VIV onset wind speed increases by 1.68 m/s, the maximum vibration amplitude decreases by 0.072, and the lock-in range decreases from 14.35-20.32 m/s to 16.03-16.93 m/s. In the range of 3.2 \(\times\) 10\({}^{4}\) < \(Re\) < 8.3 \(\times\) 10\({}^{4}\), the mean values of the wind pressure coefficients on the upper and lower surfaces of the vibrating main beam are similar to the static results, with both exhibiting a weak Reynolds number effect. Both the dynamic and static RMS values of the wind pressure coefficients on the upper and lower surfaces decrease as the Reynolds number increases; however, there are significant differences in the distribution characteristics and values along the surface.  
(3) In free vibration tests, as the Reynolds number increases, the surface RMS values of the wind pressure coefficients of the main beam decrease. The dominant frequencies in the fluctuating pressure amplitude spectra at each measurement point become more dispersed. The correlation coefficients between the aerodynamic forces at each measurement point and the VIF, as well as the contribution coefficients of the aerodynamic forces to the VIF, generally decrease. To varying extents, the aerodynamic time-frequency parameters reveal the underlying reasons for the attenuation of the main beam's VIV with increasing Reynolds numbers. In this paper, the research on the Reynolds number effect mechanism of VIV characteristics of a streamlined box girder is further improved, which provides a reference for solving practical problems.  
Conceptualization, Q.L.; data curation, B.W. and Y.H.; methodology, Z.L.; writing--original draft, B.W.; writing--review and editing, Y.S. and K.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (52408551), Natural Science Foundation of Hebei Province of China (E2022210078, E2024210071), Science and Technology Project of Hebei Education Department (QN2024038), Central Leading Local Science and Technology Development Fund Project (236Z5410G), High-End Talents Project of Hebei Province of China ([2019] 63), S&T Program of Hebei (225676162 GH), and Shijiazhuang Tiedao University graduate student innovation funding project (YC202412).  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest**: The authors declare no conflict of interest.