# Flutter Mechanism of a Thin Plate Considering Attack Angles
## 3 Flutter Calculation Results for the Thin Plate
Figures 5 and 6 show the variation curves of aerodynamic damping and modal frequency with reduced wind speed for the thin plate at different angles of attack. From the variation of aerodynamic damping (Figure 7), it can be seen that the aerodynamic damping for the torsional mode branch first reaches a 'positive-to-negative' state, meaning that the flutter characteristics of the plate from a 0\({}^{\circ}\) to 7\({}^{\circ}\) angle of attack are dominated by the torsional mode branch. The curves of aerodynamic damping with reduced wind speed show significant differences at different angles of attack, indicating that the changes in flutter derivatives directly cause substantial variations in aerodynamic damping. Although the flutter derivatives differ significantly at different angles of attack when the dynamic parameters are the same, the variation patterns of modal frequency with reduced wind speed are generally consistent, and the flutter frequency remains consistent across different angles of attack. While Figures 5 and 6 provide a macro-level understanding of how aerodynamic damping and modal frequency vary with reduced wind speed, they also highlight the complexity of the factors influencing these variations. This complexity underscores the need for further analysis, which is not only necessary but also intriguing. Given the similarity of the  
Figure 4: Flutter derivatives of the thin plate under different angles of attack. variation curves of modal frequency and aerodynamic damping with reduced wind speed for Case 1, Case 2, and Case 3, and the constraints of space, the following discussion will focus on Case 2 to delve into the flutter mechanisms of the thin plate at different angles of attack in detail. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**AAOA** & **Condition** & \begin{tabular}{c} **Measured** \\ **Reduced Wind** \\ **Speed** \\ \end{tabular} & \begin{tabular}{c} **Calculated** \\ **Reduced Wind** \\ **Speed** \\ \end{tabular} & \begin{tabular}{c} **Error** \\ **Error** \\ **Frequency** \\ \end{tabular} & \
\begin{tabular}{c} **Experimental** \\ **Flutter** \\ **Frequency** \\ \end{tabular} &
\begin{tabular}{c} **Calculated** \\ **Flutter** \\ **Frequency** \\ \end{tabular} & **Error** \\ \hline \multirow{3}{*}{0} & Case 1 & 6.13 & 6.15 & 0.32\% & 2.61 & 2.54 & 2.68\% \\  & Case 2 & 10.36 & 10.3 & 0.57\% & 3.01 & 2.88 & 4.30\% \\  & Case 3 & 12.64 & 12.7 & 0.47\% & 3.38 & 3.21 & 5.0\% \\ \hline \multirow{3}{*}{3} & Case 1 & 6.07 & 5.92 & 2.50\% & 2.59 & 2.53 & 2.31\% \\  & Case 2 & 10.06 & 9.65 & 4.10\% & 3.03 & 2.87 & 5.28\% \\  & Case 3 & 12.52 & 12.0 & 4.20\% & 3.37 & 3.19 & 5.30\% \\ \hline \multirow{3}{*}{5} & Case 1 & 5.78 & 5.83 & 0.86\% & 2.59 & 2.52 & 2.70\% \\  & Case 2 & 7.92 & 7.85 & 0.88\% & 3.07 & 2.98 & 2.93\% \\ \cline{1-1}  & Case 3 & 8.55 & 8.9 & 4.10\% & 3.53 & 3.42 & 3.10\% \\ \hline \multirow{3}{*}{7} & Case 1 & 4.68 & 4.88 & 4.30\% & 2.56 & 2.52 & 1.56\% \\ \cline{1-1}  & Case 2 & 6.02 & 6.30 & 5.10\% & 3.17 & 3.08 & 2.84\% \\ \cline{1-1}  & Case 3 & 6.57 & 6.60 & 0.45\% & 3.65 & 3.59 & 1.64\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The error analysis of critical flutter velocity. Figure 5: Flutter analysis of aerodynamic damping ratio and critical velocities of Case 1–Case 3. (**a**) 0\({}^{\circ}\) angle of attack. (**b**) 3\({}^{\circ}\) angle of attack. (**c**) 5\({}^{\circ}\) angle of attack. (**d**) 7\({}^{\circ}\) angle of attack. Figure 6: Flutter analysis of modal frequency and critical frequencies of Case 1–Case 3. (**a**) 0\({}^{\circ}\) angle of attack. (**b**) 3\({}^{\circ}\) angle of attack. (**c**) 5\({}^{\circ}\) angle of attack. (**d**) 7\({}^{\circ}\) angle of attack. Figure 7: Total damping and sub-items varying with reduced velocity.