## 3 Results and Discussion  
### Characteristics of Flutter Responses under Different Leading and Trailing Edges  
To explore the differences between the classical flutter and postflutter limit cycle vibrations, all cases with different aerodynamic configurations were conducted at an attack angle of 0\({}^{\circ}\). The relationship between the mean square root of flutter responses and reduced wind speeds were given in Figure 5. The reduced wind speeds can be calculated as  
\[U^{*}=\frac{U}{f_{\alpha 0}B} \tag{4}\]  
where \(U\) is real wind speed, \(f_{\alpha 0}\) is the torsional natural frequency, and \(B=300\) mm is the width of the sectional model. It should be noted that the relationship was obtained by changing the inflow wind speed continuously from 0 m/s, and the sectional model was not disturbed by any initial perturbation. In Figure 5, it can be seen that the shape of the leading edge had an obvious influence on flutter behavior. For the case of L30 with a streamlined leading edge, when the reduced wind speed exceeded a critical value \(U^{*}_{cr}=10.38\), the vibration amplitude of the sectional model grew rapidly and even diverged. By contrast, for the case of L180 with a bluff leading edge, the flutter critical reduced wind speed decreased significantly to \(U^{*}_{cr}=4.79\), compared with the L30 case. When the inflow velocity exceeded the critical wind speed, the vibration did not diverge rapidly. Instead, it kept its stable status, i.e., postflutter limit cycle oscillation. The stable LCO amplitude increased as the wind speed increased. Figure 4: An example of the identification results of the nonlinear structural frequency and damping ratio (Case: L30): (**a**) vertical free vibration histories; (**b**) vertical natural frequency; (**c**) vertical damping ratio; (**d**) torsional free vibration histories; (**e**) torsional natural frequency; and (**f**) torsional damping ratio. Moreover, the shape of the trailing edge had a much smaller effect on flutter behavior. When the leading-edge section was a bluff rectangle, the flutter behaviors were all characterized by the postflutter LCO, and the shape of the trailing edge slightly changed the critical wind speed and the wind speed range in which LCO occurred. The flutter critical reduced wind speed increased from \(U_{cr}^{*}=4.37\) for the case of T30 to \(U_{cr}^{*}=4.79\) for the case of L180. The displacement histories at different development stages of the two kinds of flutter and corresponding frequency spectrums are displayed in Figures 6 and 7. The frequency spectrums were obtained based on the Fast Fourier Transform method. For the classical flutter, the amplitude of flutter increased rapidly and the vibration tended to be unsteady as the development of flutter when the inflow velocity exceeded the flutter critical wind speed. However, for the postflutter LCO, a steady vibration with a stable amplitude occurred, regardless of how large the initial disturbance was when the wind speed was larger than the critical wind speed. Figure 5: Root mean square (RMS) of oscillation responses versus wind speeds; (**a**) different leading edges, vertical; (**b**) different leading edges, torsional; (**c**) different trailing edges, vertical; and (**d**) different trailing edges, torsional. (Arrow: a divergent oscillation occurs when the wind speed is larger than the critical value.). Figure 6: The response histories of the classical flutter and postflutter LCO: (**a**) classical flutter (Case: L30); and (**b**) postflutter LCO (Case: L180). Figure 7: The frequency spectrums of displacement of the classical flutter and postflutter LCO: (**a**) classical. \(U^{*}=10.47\)); and (**b**) postflutter LCO (Case: L180, \(U^{*}=6.12\)). For the two kinds of flutter, the dominant vibration frequencies were both coupled in vertical and torsional degrees of freedom. The coupling frequency \(f_{c}=3.38\) Hz for the case L30 was closer to the vertical natural frequency \(f_{h0}=3.07\) Hz than \(f_{c}=3.83\) Hz for L180.