机翼颤振的随机Hopf分岔研究

RESEARCH OF STOCHASTIC HOPF BIFURCATION ON AIRFOIL FLUTTER

建立一个机翼颤振的随机非线性模型,运用拟不可积Hamiltion相关理论,对扩散边界性态进行分析,得到全局稳定性的条件;计算并分析系统平稳概率密度和系统联合概率密度的不变测度,得到模型随机Hopf分岔的条件,结合实际进行数值仿真,得到可能导致机翼颤振的关键参数。结果表明,俯仰角的大小在一定条件下对机翼颤振问题起着重要作用。

A stochastic nonlinear dynamical model of airfoil flutter had been presented. The global stability conditions had also been obtained by using quasi non-integrable Hamiltonian theory and judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stationary and joint probability densities, and the condition of stochastic Hopf bi- furcation had been discussed. The key parameter impacting the airfoil flutter had been found by numerical emulation. The result dedicats that the angle of pitching plays an important role in some conditions.