本项目拟研究随机激励下二元机翼模型的非线性随机动力学响应。首先，以确定性二元机翼模型为基础，引入噪声更加客观地建立随机二元机翼模型，并提出新的适用于确定和随机二元机翼模型的近似解析方法，探索随机激励下机翼的动力学响应；其次，结合已有的单自由度低维随机动力学理论，以随机二元机翼模型为研究对象，提出合理的随机分岔和首次穿越的定义，应用FPK方程、概率密度函数等手段讨论随机二元机翼模型的跃迁行为，阐述噪声对二元机翼模型动力学的影响规律；然后，针对随机机翼模型可能出现的颤振问题，建立不同噪声激励下二元机翼模型的控制器，有效抑制机翼的颤振现象，并应用Lyapunov稳定性理论分析系统的稳定性；最后，将高斯白噪声和窄带噪声激励下二元机翼模型的理论，推广到具有相关时间的高斯色噪声和具有大跳跃的列维噪声上，揭示不同于以往高斯白噪声对二元机翼模型的作用机理，为航空领域的发展奠定基础和提供潜在的理论支持。

Nonlinear stochastic dynamical responses of the two-degree-of-freedom airfoil (TDOFA) models will be investigated. Firstly, based on the deterministic airfoil models, we will introduce the random fluctuations to establish the new stochastic TDOFA models, and new approximate method is proposed to investigate the dynamical responses of the given deterministic and stochastic TDOFA systems. Secondly, with the theories of single-degree-of-freedom and low dimensional systems, we concentrate on the definitions of stochastic bifurcation and first passage on the topics of our stochastic TDOFA models. Applying the techniques of Fokker-Planck equation and probability density function, the stochastic transition phenomena of TDOFA models are studied with the mechanisms of random noise. Thirdly, controllers are designed with respect to different types of noise to restrain the flutter of airfoil, and the Lyapunov stability theory is conducted to analyze the stability of TDOFA models. Finally, we extend the obtained results to colored Gaussian noise with correlation time and Lévy noise with big jumps, and illustrate the different mechanisms which differ from those of Gaussian white noise and narrow-band noise. The results and methods in this project will be regarded as the foundation and the potential theoretical supports for the development of aviation area.