## 3 Validations and Applications
### Practical Application  
Since the main girder sections of most actual bridges are more significantly blunted than that of GBEB, this paper takes LDYB, a suspension bridge with a main span of 1666 m under construction in Guangdong, China, as another engineering background to further study the accuracy of using the Volterra series-based ROM model to describe the aerodynamic nonlinearity of the main deck section with crash barriers. LDYB is an essential part of the Shenzhen-Zhongshan Link Project, which is one of China's critical cross-river projects and is of great significance to their economic development. Figure 11 shows the original main deck section of LDYB. As shown in Figure 11, the width and height of the main deck section are 49.7 m and 4.0 m, respectively. Compared with the case of the GBEB, the main deck section of LDYB includes sidewalk outriggers, crash barriers, and inspection rails, where the nonlinear aerodynamic will be more foreseeably significant. The computation domain, boundary conditions, and blocks are set in Figure 3. The geometric scale ratio of the main deck section is 1:70. The height of the grid on the first layer is 0.2 cm, which is about 4 \(\times\) 10\({}^{-5}\)\(B\), and there are 312580 grids in total. Figure 12 indicates the local division of the grids near the main deck section of LDYB. The wind speed ratio is 1:4.16, the incoming wind speed is \(U=18\) m/s for the Volterra kernels identification, and the corresponding wind speed at the bridge is 75 m/s, which is close to the flutter critical wind speed of the LDYB section for subsequent flutter analysis. The rest of the calculation parameters are set the same as in the case of GBEB. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Flutter Critical Wind Speed (m/s)** & **Flutter Frequency (Hz)** \\ \hline Finite volume method & 40.5 & 0.160 \\ ([PERSON] [29]) & 37.6 & 0.165 \\ Discrete-vortex model & 36.0 & 0.163 \\ ([PERSON] [30]) & 35.0 & 0.160 \\ Wind tunnel test & 40.0 & 0.164 \\ ROM (present) & 35.0\(-\)40.0 & 0.160 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons of flutter results of the girder of GBEB. Figure 11: Girder cross-section of LDYB main span (unit: mm). To study the first-order Volterra model in more nonlinear aerodynamic conditions, the wind-induced vibration responses of the main deck section of LDYB for different wind speeds near the flutter critical wind speed are calculated by ROM and FSI, respectively. The main parameters of the main deck section of LDYB are given in Table 5.  
Figure 13 shows the numerical results of wind-induced vibration responses of the main deck section by ROM method for incoming wind speeds of 75 m/s and 80 m/s for the prototype main deck section, respectively. As shown in Figure 13, when the incoming wind speed is 75 m/s for the prototype main deck section, the torsional displacement and vertical displacement of the prototype girder have no obvious flutter divergence phenomenon. However, when the incoming wind speed is 80 m/s for the prototype main deck section, the torsional displacement and vertical displacement of the girder have an apparent flutter divergence phenomenon. Therefore, the calculation result of the flutter critical wind speed of the main girder section of LDYB obtained by the ROM method is about 75-80 m/s. Figure 12: Local mesh division of the computational domain (**a**) near the main deck section; (**b**) near the maintenance vehicle tracks; and (**c**) near the sidewalk outriggers.