This paper investigates the effects of the unsteady nonlinear aerodynamic, plunge/pitch cubic nonlinearities, flap free-play nonlinearity, and coupled nonlinear aeroelasticity on the dynamics of the three-dimensional blade section. The dynamic stall model is developed based on the unsteady Wagner aerodynamics. Coupling the developed nonlinear aerodynamic model and nonlinear elasticity model results in the nonlinear aeroelastic model. The nonlinear aeroelastic equation of motion is converted into a state-space form. The resulting nonlinear state-space equation of motion is simulated by a standard Runge–Kutta algorithm in MATLAB. The proposed model is validated against test data of distinct two- and three-degrees-of-freedom studies and is compared to the ONERA model. Bifurcation diagrams show that there is distinct airspeed, in which the system experiences limit cycle oscillations (LCOs) or chaos. Both hysteresis air loads and structural nonlinearity make the system unstable at airspeed less than linear flutter speed. The nonlinearity of the structure causes supercritical pitchfork bifurcation. Elastic-aerodynamic nonlinearity interaction causes sub-supercritical bifurcation at the lower airspeed and chaotic motion at a higher airspeed. Furthermore, the effects of the initial condition on the response of the nonlinear aero-servo-elastic system are investigated by the Lyapunov exponent method.

中文翻译：

---

一种新的动态失速方法，用于研究带襟翼自由运动部分的叶片部分气动弹性响应中的分叉和混沌

本文研究了非定常非线性气动、俯冲/俯仰三次非线性、襟翼自由游隙非线性和耦合非线性气动弹性对三维叶片截面动力学的影响。动态失速模型是在非定常瓦格纳空气动力学的基础上发展起来的。将所开发的非线性气动模型和非线性弹性模型耦合，得到非线性气动弹性模型。非线性气动弹性运动方程被转换为状态空间形式。由此产生的非线性状态空间运动方程通过 MATLAB 中的标准 Runge-Kutta 算法进行模拟。所提出的模型针对不同的二自由度和三自由度研究的测试数据进行了验证，并与 ONERA 模型进行了比较。分岔图显示有明显的空速，系统经历极限循环振荡 (LCO) 或混沌。滞后空气载荷和结构非线性都使系统在空速低于线性颤振速度时不稳定。结构的非线性导致超临界干草叉分叉。弹性-气动非线性相互作用导致较低空速下的亚超临界分叉和较高空速下的混沌运动。此外，利用Lyapunov指数法研究了初始条件对非线性气动伺服弹性系统响应的影响。弹性-气动非线性相互作用导致较低空速下的亚超临界分叉和较高空速下的混沌运动。此外，利用Lyapunov指数法研究了初始条件对非线性气动伺服弹性系统响应的影响。弹性-气动非线性相互作用导致较低空速下的亚超临界分叉和较高空速下的混沌运动。此外，利用Lyapunov指数法研究了初始条件对非线性气动伺服弹性系统响应的影响。