# Steady-Suction-Based Flow Control of Flutter of Long-Span Bridge
## 3 Results and Discussion
### Effects of Steady-Suction-Based Flow Control on Flutter Derivatives  
Based on Equation (1), the FDs are transfer functions of bridge displacements to self-excited forces that might lead to flutter. They are regarded as indicators of the bridge deck flutter susceptibility. Therefore, they are often employed to assess the aerodynamic stability of structures. The purpose of this part is to discuss the effects of steady-suction flow control on FDs to theoretically analyze the control mechanism. All eight FDs, i.e., \(H_{1}^{*}-H_{4}^{*}\) and \(A_{1}^{*}-A_{4}^{*}\), of the different cases extracted through the ILS method are presented in Figures 5-10 as functions of the reduced wind velocity \(U_{r}=U/f_{v}B\), where \(U\) is the oncoming-wind velocity, \(f_{v}\) is the vertical frequency of the dynamic system, and \(B\) denotes the model width. The FDs were normalized with respect to the vertical natural frequency of the oscillation (\(H_{1}^{*}\), \(H_{4}^{*}\), \(A_{1}^{*}\), \(A_{4}^{*}\)) and the torsional natural frequency of the oscillation (\(H_{2}^{*}\), \(H_{3}^{*}\), \(A_{2}^{*}\), \(A_{3}^{*}\)). The results for \(H_{i}^{*}\) (\(i=1-4\)) and \(A_{i}^{*}\) (\(i=1-4\)) are presented and discussed separately. Figure 4: Flutter derivatives (FDs) extracted by the present experiment and comparison with results obtained by [PERSON] et al. [21] and [PERSON] [22]. (**a–d**) \(A_{i}^{*}\) (\(i=1-4\)); (**e–h**) \(H_{i}^{*}\) (\(i=1-4\)). Figure 5: (**a–d**) Flutter derivatives \(H_{i}^{*}\) (\(i=1-4\)) for test cases with different suction positions. Figure 6: (**a–d**) Flutter derivatives \(H_{i}^{*}\) (\(i=1-4\)) for test cases with different suction intervals. Figure 8: (**a-d**) Flutter derivatives \(A_{i}^{*}\) (\(i=1-4\)) for test cases with different suction positions. Figure 7: (**a-d**) Flutter derivatives \(H_{i}^{*}\) (\(i=1-4\)) for test cases with different suction flow rates. Figure 10: (**a–d**) Flutter derivatives \(A_{i}^{*}\) (\(i=1-4\)) for test cases with different suction flow rates. Figure 9: (**a–d**) Flutter derivatives \(A_{i}^{*}\) (\(i=1-4\)) for test cases with different suction intervals. The \(H_{1}^{*}\) derivative is an important FD for the analysis of the heave motion because it is associated with aerodynamic damping in a heave motion; \(H_{1}^{*}\) is positive for negative aerodynamic damping, which indicates a potential dynamic instability of the bridge deck section. To be specific, if the negative aerodynamic damping is stronger than the positive structural damping, the total heave damping (the sum of aerodynamic damping and mechanical damping of a structure) in the heave motion becomes negative. In this case, any external disturbance to the system can lead to divergent oscillations or even the collapse of the bridge. The trends of \(H_{1}^{*}\) were similar for the cases with different suction slot positions (i.e., _l_-_2d_-10, _m_-_2d_-10, _b_-_2d_-10, and \(s\)00; Figure 5a): \(H_{1}^{*}\) gradually decreased with increasing reduced wind speed from 2.08 to 13.68. When \(U_{r}<8\), the suction position influenced the \(H_{1}^{*}\) derivative negligibly. However, when the reduced wind speed exceeded 8, the negative slope of _l_-_2d_-10 became steeper than those of the other two cases (_m_-_2d_-10 and _b_-_2d_-10). Thus, activating the suction slots on the windward side is the best choice to effectively reduce the negative aerodynamic damping of the bridge deck. For cases with different suction intervals (i.e., _l_-_1H_-5, _l_-_2d_-5, _l_-_3d_-5, _l_-_4d_-5, and \(s\)00; Figure 6a), the trends of \(H_{1}^{*}\) were approximately equal. Generally, the values of _l_-_1d_-5 and _l_-_2d_-5 were lower than those of the other cases, particularly in the range \(U_{r}\approx 10-14\). This implies that shorter suction intervals tend to alleviate negative aerodynamic damping, which enhances the flutter performance of the bridge.