A computational study of forced aeroelastic system of an airfoil is performed under various free-stream velocities. The results show that, as the free-stream velocity increases, the natural frequency of the system is increasing due to the aerodynamic stiffness effect except for a certain velocity range where the sub-harmonic synchronization occurs. To explore the characteristics of aerodynamic stiffness alone, the free oscillation response under the same conditions are simulated. The simulation shows that the aerodynamic stiffness presents a non-monotonic characteristic with the increase of the free-stream velocity. Further investigation indicates that the trend of aerodynamic stiffness varying with free-stream velocity is closely related to different areas at which the minimum angle of attack is located, which are greater than zero, less than zero or less than the dynamic stall angle in opposite direction. Equivalent linearization analysis qualitatively explains the reasons for the different aerodynamic stiffness characteristics in the above three phases. Comparing the results of the forced and the free system, it is found that the natural frequency under the influence of aerodynamic stiffness in the second stage is close to the 1/2 sub-harmonic of forcing frequency, resulting in the sub-harmonic synchronization. Moreover, the occurrence of dynamic stall in the opposite direction is considered to be the mechanism of unlock from the 1/2 sub-harmonics of forcing frequency.

机翼受迫气动弹性系统的计算研究是在各种自由流速度下进行的。结果表明，随着自由流速度的增加，系统的固有频率由于空气动力学刚度效应而增加，除了发生次谐波同步的一定速度范围外。为了单独探索气动刚度的特性，模拟了相同条件下的自由振荡响应。仿真结果表明，随着自由流速度的增加，气动刚度呈现非单调特性。进一步研究表明，气动刚度随自由流速度变化的趋势与最小迎角所在的不同区域密切相关，它们大于零，小于零或小于相反方向的动态失速角。等效线性化分析定性解释了上述三个阶段气动刚度特性不同的原因。对比受迫系统和自由系统的结果，发现第二阶段气动刚度影响下的固有频率接近受迫频率的1/2次谐波，导致次谐波同步。此外，相反方向的动态失速的发生被认为是从强迫频率的1/2次谐波解锁的机制。等效线性化分析定性解释了上述三个阶段气动刚度特性不同的原因。对比受迫系统和自由系统的结果，发现第二阶段气动刚度影响下的固有频率接近受迫频率的1/2次谐波，导致次谐波同步。此外，相反方向的动态失速的发生被认为是从强迫频率的1/2次谐波解锁的机制。等效线性化分析定性解释了上述三个阶段气动刚度特性不同的原因。对比受迫系统和自由系统的结果，发现第二阶段气动刚度影响下的固有频率接近受迫频率的1/2次谐波，导致次谐波同步。此外，相反方向的动态失速的发生被认为是从强迫频率的1/2次谐波解锁的机制。