## 3 Wind Tunnel Test of Section Model
### VIV Responses of Original Section  
VIV usually occurs at lower wind speeds, and its vibration forms are divided into vertical VIV and torsional VIV. This test aims to measure the onset wind speed of VIV, the locking range of VIV wind speed, and the amplitude of VIV. This test was carried out in a uniform flow field; the test wind speed was 0 m/s\(\sim\)12 m/s, the wind attack angle was 0\({}^{\circ}\), \(\pm\)3\({}^{\circ}\), and \(\pm\)5\({}^{\circ}\), and the speed step was 0.03 m/s\(\sim\)0.13 m/s. Under the working conditions of 0\({}^{\circ}\), \(\pm\)3\({}^{\circ}\), and \(\pm\)5\({}^{\circ}\) wind attack angles, the relationship between the maximum vertical and torsional amplitudes of the main girder and the wind speed is shown in Figure 8. Obvious VIV was observed at +3\({}^{\circ}\) and +5\({}^{\circ}\) wind attack angles, among which the vertical VIV had a relatively apparent locking range. In contrast, the torsional VIV had minor and major locking ranges.  
It can be seen from Figure 8 that no matter whether it was the locking range of vertical VIV or the major locking range of torsional VIV, the maximum amplitude of VIV at a +5\({}^{\circ}\) attack angle was significantly greater than that at a +3\({}^{\circ}\) attack angle. However, for the minor locking range of torsional VIV, its maximum amplitude was not significantly affected by the attack angle. When vertical VIV occurred on the bridge, the onset wind speed at a +5\({}^{\circ}\) attack angle was earlier, and the locking range was longer than that at a +3\({}^{\circ}\) attack angle. Generating a more obvious vertical VIV in the low wind speed range was easier. When torsional VIV occurred on the bridge, the onset wind speed at a +5\({}^{\circ}\) attack angle was  
Figure 8: VIV responses of the original section of the truss girder.  
Figure 7: Equipment used in wind tunnel test.  
obviously delayed compared with a +3\({}^{\circ}\) attack angle, the length of the major locking range was significantly increased, and the maximum amplitude of the VIV was also significantly increased. No obvious VIV was observed at 0\({}^{\circ}\), -3\({}^{\circ}\), and -5\({}^{\circ}\) attack angles. At a +3\({}^{\circ}\) attack angle, the locking range of vertical VIV was 5.24 m/s-6.72 m/s, and the locking ranges of torsional VIV were 8.13 m/s-9.52 m/s and 12.27 m/s-18.06 m/s. At a +5\({}^{\circ}\) attack angle, the locking range of vertical VIV was 5.01 m/s-6.69 m/s, and the locking ranges of torsional VIV were 8.53 m/s-10.01 m/s and 13.75 m/s-19.49 m/s.  
The Fourier transform converts a time-domain signal into a frequency-domain signal, which decomposes a signal into a superposition of sine waves of different frequencies. FFT is a fast calculation method of the Fourier transform that utilizes the symmetry and periodicity of the Fourier transform, reduces computational complexity, and greatly improves computational efficiency. Through FFT in Origin 2018 software, the change in amplitude with time measured by the two laser displacement sensors in Figures 9 and 10 is converted into the change in amplitude with frequency. Figures 9 and 10 show the displacement time series and amplitude spectra of two measuring points at +3\({}^{\circ}\) and +5\({}^{\circ}\) attack angles when the displacement amplitudes of vertical VIV and torsional VIV are the largest.  
It can be seen from Figure 9 that the phases of the time history curves measured by the two sensors were the same, and the primary frequency of vertical VIV was 2.227 Hz, which was close to the vertical VIV frequency of the test model. It can be seen from Figure 10 that the phases of the time history curves measured by the two sensors were opposite, and the primary frequency of torsional VIV was 4.289 Hz, which was close to the torsional VIV frequency of the test model.