# Numerical Analysis on Spanwise Correlation of Vortex-Induced Force of Split Double-Box Beam
## 4 Results and Analysis
### Analysis of the Results of Three-Dimensional Vortex-Induced Vibration  
#### 4.3.1 Spanwise Correlation of Aerodynamic Coefficients When the Bridge Is in the Vibrational State  
The response of vortex-induced vibration of split double-box beam is numerically simulated by the dynamic-grid technology under three kinds of reduced wind velocities of 5.65, 6.21 and 6.68. Aerodynamic force is composed of external excitation force and self-excitation force related to vibration in the vibrational state. Therefore, Formula (4) is used to fit the numerical simulation results of the spanwise correlation coefficients of aerodynamic coefficients of the main beam section. The results are shown in Table 5 and Figure 11.  
It can be seen in Table 5 and Figure 11:  
* The same as that in the static state, the spanwise correlation of aerodynamic coefficients decreases with the increase of the spanwise length in the vibrational state. The attenuation speed of the lift is the slowest, the torque is the second, and the resistance is the fastest. * The spanwise correlation length of the lift coefficient is the largest, that of the resistance coefficient is second and that of the resistance coefficient is the smallest in the vibrational state. However, the spanwise correlation length of aerodynamic coefficients are smaller than those in the static state. Moreover, compared to those in the static state, the spanwise correlation coefficient of the aerodynamic coefficients of the split double-box beam is significantly larger in the vibrational state, and the attenuation speed is smaller under the same spanwise spacing. A possible reason is that in addition to the forced load of the wind velocity, the vortex-induced force in the vibrational state includes the self-excited force caused by the vibration of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Aerodynamic Coefficient**} & \multicolumn{4}{c}{**Reduced Wind Velocity**} \\ \cline{3-5}  & & **5.65** & **6.21** & **6.68** \\ \hline \multirow{3}{*}{(attenuation coefficient)} & lift coefficient & 0.119 & 0.118 & 0.107 \\  & resistance coefficient & 0.339 & 0.437 & 0.386 \\  & torque coefficient & 0.159 & 0.143 & 0.148 \\ \hline \multirow{3}{*}{(spanwise correlation length)} & lift coefficient & 0.371 & 0.396 & 0.386 \\  & resistance coefficient & 0.225 & 0.251 & 0.240 \\  & torque coefficient & 0.396 & 0.388 & 0.291 \\ \hline \multirow{3}{*}{(horizontal asymptote of the function)} & lift coefficient & 8.437 & 8.475 & 9.346 \\  & resistance coefficient & 2.950 & 2.288 & 2.591 \\ \cline{1-1}  & torque coefficient & 6.289 & 6.993 & 6.757 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fitting value of aerodynamic spanwise correlation coefficient parameters and spanwise correlation length of the main beam in the vibrational state. structure as well. Therefore, the self-excited force has a great influence on the spanwise correlation of the vortex-induced force. 3.2 Spanwise Correlation of Surface Pressure Coefficient When the Bridge Is in the Vibrational State  
Two measurement points, which are shown in Figure 8, were selected in this section to study the correlation of the pressure coefficient in the vibrational state when the reduced wind velocity is 5.65 and 6.21. The variation of the spanwise correlation coefficient of the pressure coefficient with the spanwise spacing is shown in Figure 12.  
It can be found in Figure 12 that:  
* The spanwise correlation of the model surface pressure in the wake region in vibration is relatively higher. The spanwise correlation coefficient decreases with the increase of spanwise spacing firstly and then fluctuates around a certain value. * As with that in the static state, the spanwise correlation of the pressure coefficient of the upstream panel is higher than that of the downstream panel in the vibrational state.