超声速二元机翼随机混沌运动分析

以考虑随机扰动的超声速二元机翼为研究对象,采用Kapitaniak方法对超声速二元机翼的随机混沌特性进行研究。采用三阶活塞理论推导超声速二元机翼的非线性气动力和气动力矩,建立考虑随机扰动、具有俯仰立方非线性的机翼2自由度运动微分方程,并将其写成4维状态方程的形式;采用中心流形方法对系统进行降维,将系统状态方程从4维降为2维;再联合利用累积量截断法、非高斯截断法获得系统的二维联合概率密度函数及系统的概率时差图,采用Kapitaniak方法分析系统在不同扰动强度下的随机混沌特性;采用系统响应、庞加莱截面图及最大Lyapunov指数等对系统的随机混沌特性进行验证。本研究对超声速二元机翼在复杂环境下的稳定性、安全性及响应特性等研究具有重要的促进作用。

Analysis of stochastic chaotic motion on supersonic two-dimensional airfoil

The stochastic chaotic characteristics of supersonic two-dimensional airfoil were studied by Kapitaniak method. Nonlinear aerodynamics and aerodynamic moments of supersonic two-dimensional airfoil were deduced by the third-order piston theory. The 2 degree of freedom differential equation of motion of the airfoil with pitch cubic nonlinearity under stochastic disturbance was established and written in the form of 4-dimensional state equation. Then the system state equation was reduced to 2-dimensional by using the central manifold method. After that, the combination of the methods of cumulant neglect and non-Gauss truncated was used to obtain the two-dimensional probability density function and the probabilistic time-difference diagram of the system. Therefore, the Kapitaniak method was used to analyze the stochastic chaotic characteristics of the system under different disturbance intensities. Finally, the system response, Poincare cross-section diagram and the largest Lyapunov exponent were used to verify the stochastic chaotic characteristics of the system. The research is very important for the stability, safety and response characteristics of the supersonic two-dimensional airfoil in complex environment.