## 3 Vortex-Induced Vibration Performance with Different Vortex Isolation Plates  
Figure 4 presents the impact of vortex isolation plates with 10 mm and 20 mm opening sizes on the performance under heaving VIVs in twin-box girders under varying opening ratios. The results show that, with a decrease in the opening ratio, the twin-box girder's performance under VIVS is gradually enhanced. As shown in Figure 4a,b, VIVs occur when the opening ratio is 48.68% at a 0\({}^{\circ}\) AOA. Notably, the vibration amplitude of the plate with a 10 mm circular opening is greater than that of the plate with a 20 mm circular opening. At a +3\({}^{\circ}\) AOA, both the plates with 10 mm and 20 mm circular openings exhibit similar vibration phenomena. Specifically, at an opening ratio of 23.40%, both plates experience \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & **Type of Vortex** & **Opening** & \multirow{2}{*}{**AOA**} & **Opening** & **Single Opening** \\  & **Isolation Plates** & **Ratio (\%)** & & **Number** & **Area (mm\({}^{2}\))** \\ \hline
1 & No plate & 100\% & & - & - \\
2 & No opening & 0\% & 0 & 0 \\
3–5 & & 9.35\% & & 68 & \\
6–8 & Plate with & 23.40\% & & 170 & \\
9–11 & 20 mm opening & 35.48\% & & 258 & 314.16 \\
12–14 & diameter & 48.68\% & 0\({}^{\circ}\) & 354 & \\
15–17 & & 64.36\% & +3\({}^{\circ}\) & 468 & \\
18–20 & & 9.35\% & -3\({}^{\circ}\) & 272 & \\
21–23 & Plate with & 23.40\% & & 680 & \\
24–26 & 10 mm opening & 35.48\% & & 1032 & 78.54 \\
27–29 & diameter & 48.68\% & & 1416 & \\
30–32 & & 60.37\% & & 1756 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test cases of different vortex isolation plates in combined vibration–pressure tests. Figure 3: Plates with different opening ratios. (**a**) \(\gamma=0\%\) or \(100\%\), (**b**) opening diameter d = 20 mm, and (**c**) opening diameter d = 10 mm. low-amplitude VIVs at high wind velocities. The effect of the opening ratio on the VIVs at a \(-3^{\circ}\) AOA is similar to that observed at a \(0^{\circ}\) AOA; however, the amplitude of the former is larger. Notably, the VIV phenomenon occurs at an opening ratio of 35.48%. This suggests that the opening ratio plays a significant role in determining the magnitude of heaving VIVs, particularly when it comes to varying the AOA. As the AOA shifts from positive to negative, the influence of the opening ratio gradually intensifies. Additionally, at the same opening ratio, the performance under VIVs is affected by the opening size of the vortex isolation plate, which can lead to deterioration in the vibration amplitude. This phenomenon emphasizes the importance of carefully considering the opening size when designing a vortex isolation plate. Figure 5 illustrates the torsional vibration response at different AOAs for different opening ratios. It appears that the impact of the vortex isolation plate on torsional vibrations is not the same as that on heaving vibrations. At a \(0^{\circ}\) AOA, at the same opening ratio, the vortex isolation plate with a 10 mm opening size is more likely to exacerbate the torsional VIVs compared to the vortex isolation plate with a 20 mm opening size. When the opening ratio falls between 23.40% and 60.37%, the vortex isolation plate with a 10 mm opening induces torsional VIVs, whereas the vortex isolation plate with a 20 mm opening does not. This observation suggests that the opening size of the vortex isolation plate can significantly impact the performance under torsional VIVs within a certain opening ratio range. At a \(+3^{\circ}\) AOA, the torsional amplitude of the twin-box girder is marginally suppressed as the  
Figure 4: Heaving vortex-induced vibration response of different AOAs using different vortex isolation plates with different opening ratios. (**a**,**b**) \(0^{\circ}\) AOA, (**c**,**d**) \(+3^{\circ}\) AOA, and (**e**,**f**) \(-3^{\circ}\) AOA; the opening diameter is d = 20 mm in (**a**,**c**,**e**), while the opening diameter is d = 10 mm in (**b**,**d**,**f**).