间隙非线性颤振系统的极限环及复杂响应分析方法研究

Airfoil flutter analysis is a key aspect for the fight vehicle design. The analysis of vibration of the airfoil in the lifting and landing phases is crucial, since the vibration is most significant and a big amount of accidents occur at this stage. In general, the lifting and landing speed of the airliners is less than 0.3 Mach, which belongs to low subsonic range. In this speed range, the aerodynamic forces can be expressed by the potential flow theory explicitly, so a simple dynamical model can be established for the present problem, rendering a possibility for analyzing its complex responses. In this study, using NACA0012 as the prototype, a two dimensional airfoil under incompressible flow is analyzed to show the periodic and complex responses of the airfoil in lifting and landing phases. Concretely, the main research contents include: establishing the nonlinear dynamical model of the airfoil with a freeplay flap undergoing incompressible subsonic flow; developing an efficient and accurate time domain collocation method to obtain the periodic responses; introducing Henon’s method to handle the freeplay nonlinearity of the present system so as to achieve accurate simulation results for both periodic and complex responses; using Poincare map, largest Lyapunov exponent to identify and analyze chaos and route to chaos, and then analyzing the parameter effects on dynamical responses. This study can provide valuable guidance to the airfoil design of China’s airliners.

机翼颤振分析是飞行器设计的关键环节，机翼在起飞和降落阶段振动最为剧烈，是事故多发阶段，对其研究有重要意义。大型客机的起飞和着陆速度小于0.3马赫，属低亚音速飞行，在该速度范围内的气动力可用不可压缩流理论进行显式描述，便于建立机翼颤振简化模型，从而使对机翼的复杂响应研究成为可能。本课题以NACA0012为模型机翼展开理论分析，主要研究低亚音速不可压缩流场中含有操纵面间隙非线性的机翼颤振模型的周期振动和复杂响应。研究内容包括：建立考虑操纵面间隙非线性的机翼颤振动力学模型；发展高效、高精度的时域配点法快速求解动力学系统周期解；引入Henon法处理间隙非线性常微分方程，求得高精度数值解；使用Poincare映射图、最大Lyapunov指数法研究系统的混沌等复杂响应，然后研究飞行速度、非线性强弱、间隙大小等参数对动力学响应的影响。本研究将为我国大型客机在起飞、降落阶段的机翼颤振研究提供理论指导。

本项目针对机翼非线性颤振的工程实际非线性动力学问题，提出了一种基于时域配点离散思想的拓展时域配点法，大大提高了亚音速下非线性机翼颤振系统的求解效率和精度。根据项目任务书的要求，本项目具体开展的研究内容包括以下几个内容：（1）以NACA0012为模型机翼展开理论分析，使用经典拉格朗日方程建立了考虑操纵面间隙非线性的机翼颤振动力学模型；（2）基于配点离散的思路，提出了高效高精度的时域配点法，从而快速求解机翼颤振动力学系统周期解，并通过增加配点个数推导了拓展时域配点法，成功消除了“非物理解”现象，将计算精度提高30%以上；（3）由于间隙非线性的存在，传统数值积分方法在解算过程中会因跨越间隙切换点而产生系统误差，本项目中引入Henon法处理间隙非线性常微分方程，求得了高精度数值解；（4）使用Poincare映射、最大Lyapunov指数法研究系统的混沌等复杂响应，然后研究了弹性轴位置、非线性强弱、间隙大小等参数对动力学响应的影响。本项目在研究过程中主要贡献有两点：（1）基于配点离散的思想，提出了适应于求解强非线性动力学系统的高效高精度拓展时域配点法；（2）提出了一种最大李雅普诺夫观察法，可以有效的预测机翼颤振的混沌边界，提高了机翼设计的参数优化设计效率。总之，本研究为我国大型客机在起飞、降落阶段的机翼颤振研究提供理论指导。