航空学报 > 2010, Vol. 31 Issue (10): 1946-1952

二元非线性机翼随机动力学行为

黄勇1, 方次军1,2, 刘先斌1   

  1. 1. 南京航空航天大学 航空宇航学院2. 湖北工业大学 理学院
  • 收稿日期:2009-12-03 修回日期:2010-03-02 出版日期:2010-10-25 发布日期:2010-10-25
  • 通讯作者: 刘先斌

On Stochastic Dynamical Behaviors of Binary Airfoil with Nonlinear Structure

Huang Yong1, Fang Cijun1,2, Liu Xianbin1   

  1. 1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics2. School of Science, Hubei University of Technology
  • Received:2009-12-03 Revised:2010-03-02 Online:2010-10-25 Published:2010-10-25
  • Contact: Liu Xianbin

摘要: 为考查在高斯白噪声作用下二元机翼随机颤振动力学行为,采用数值仿真的方法对其进行了研究。首先把机翼简化成一个具有扭转和上下自由度的平板,其中扭转弹簧具有3次非线性刚度,同时假设空气是线性不可压的而且气动力是定常的,再对任意运动和高斯白噪声作用下的机翼进行建模。其次采用了蒙特卡罗仿真来求解随机微分方程的数值解,根据数值解结果进行统计分析,计算出最大Lyapunov指数。最后得出:在随机激励作用下机翼的动力学行为与确定性颤振相比有很大差异,同时随机颤振点提前于确定性颤振点。

关键词: 随机颤振, 非线性系统, 随机分叉, 白噪声, Lyapunov指数

Abstract: This article examines the dynamical behavior of stochastic flutter of binary airfoil that is excited by a Gauss white noise by means of numerical simulation. Firstly, the airfoil is modeled as a flat plate in a linear constant incompressible flow under a Gauss white noise excitation. The plate is with two degrees of freedom on heave and pitch and with a structural type nonlinearity in the form of a cubic hardening torsional spring. Secondly, a Monte Carlo simulation is performed to solve the system of random differential equations. And then based on the numerical result, a statistic analysis is made and the maximal Lyapunov exponent of the relevant system is obtained. Finally, it is found that the dynamical behavior of a nonlinear structural airfoil excited by a Gauss white noise is dramatically different from that of a deterministic system and its stochastic flutter point is always ahead of the point of the deterministic flutter.

Key words: stochastic flutter, nonlinear system, stochastic bifurcation, white noise, Lyapunov exponent

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