# 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
For cases with variable suction flow rate (i.e., _l_-_2d_-5, _l_-_2d_-7, _l_-_2d_-10, and \(s\)00; Figure 7a), the trends of \(H_{1}^{*}\) were still similar; the value decreased with increasing wind velocity. However, for _l_-_2d_-10, \(H_{1}^{*}\) was significantly lower than those of the other cases, resulting in the lowest negative aerodynamic damping. This explains why a higher suction rate leads to a better control effect. The \(H_{2}^{*}\) derivative is an indirect coefficient used to interpret the effect of the torsional aerodynamic damping on the heave motion. If \(H_{2}^{*}\) is positive, the aerodynamic instability phenomenon might occur owing to negative aerodynamic damping. As shown in Figure 5b, installing the control equipment on the windward side (_l_-_2d_-10) reduced the negative aerodynamic damping to a certain extent. However, for the remaining cases with control (_b_-_2d_-10 and _m_-_2d_-10), the installation did not cause great differences with respect to the single-deck case. Moreover, as seen in Figures 6b and 7b, the \(H_{2}^{*}\) derivative was not significantly affected by the other two control variables (such interval and suction flow rate). The trends of \(H_{2}^{*}\) of all the studied cases were approximately equal; they increased with increasing reduced wind speed. Please note that \(H_{2}^{*}\) was negative when the wind speed was relatively low. However, \(H_{2}^{*}\) became positive as the wind speed increased to a certain value, which is worthy of attention. According to Equation (1), the \(H_{3}^{*}\) derivative is related to the aerodynamic stiffness in the pitch motion. A positive \(H_{3}^{*}\) leads to negative aerodynamic stiffness, thereby adversely affecting the aerodynamic stability of the bridge deck. As shown in Figures 5c, 6c and 7c, the steady-suction control system increased \(H_{3}^{*}\), which resulted in a decrease in the total stiffness of the bridge. Nevertheless, \(H_{3}^{*}\) remained almost constantly negative. Hence, a negative aerodynamic stiffness cannot be generated with or without a control system. Although the presented control method reduced the net stiffness in the pitch motion, it did not deteriorate the flutter performance of the bridge. According to Figures 5d, 6d and 7d, the \(H_{4}^{*}\) derivative exhibited a relatively unpredictable behavior in all the studied cases owing to its sensitivity to the input-signal noise. High absolute values of this derivative generally indicate adverse differences in the natural frequency of the oscillations in the heave motion with respect to the initial condition at zero reduced velocity. This was not observed for the presented test cases with or without a control system and requires further investigation. The indirect \(A_{1}^{*}\) derivative is associated with the aerodynamic damping in the heave motion caused by torsional motion. As for \(H_{1}^{*}\), a positive \(A_{1}^{*}\) leads to negative aerodynamic heave damping. As depicted in Figures 8a, 9a and 10a, \(A_{1}^{*}\) exhibited an upward trend with increasing wind speed, and \(A_{1}^{*}\) of all the cases were similar for \(U_{r}\approx 2-8\). However, when the reduced wind velocity \(U_{r}\) exceeded 8, the control system applied to reduce \(A_{1}^{*}\) strengthened the total damping. To be specific, regarding the cases _l_-_2d_-10, _m_-_2d_-10, and _b_-_2d_-10, the values of \(A_{1}^{*}\) of _l_-_2d_-10 were generally below those of the other cases, which explains why the windward side is the best choice. In addition, for the cases with different suction intervals (Figure 9a), the values of cases with shorter intervals (_l_-_1d_-5 and _l_-_2d_-5) were generally lower than those of the cases with longer intervals (_l_-3_d_-5 and _l_-4_d_-5). Thus, a shorter interval is the better choice. Regarding the cases with different suction flow rates (Figure 9(a)), the growth rate of \(A_{1}^{*}\) decreased with increasing suction flow rate. Thus, increasing the suction flow rate reduces the negative aerodynamic damping, and flutter can be avoided.