具有间隙非线性的二元机翼的随机分岔和功率谱分析

赵德敏;张琪昌;王炜

振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 86-89.

振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 86-89.
论文

具有间隙非线性的二元机翼的随机分岔和功率谱分析

  • 赵德敏, 张琪昌, 王炜
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RANDOM BIFURCATION AND POWER SPECTRUM ANALYSIS OF A 2-DOF AIRFOIL WITH FREEPLAY NONLINEAR IN PITCH

  • ZHAO Demin, ZHANG Qichang, WANG Wei
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摘要

研究了在纵向和垂向随机激励联和作用下,在俯仰方向具有间隙非线性的二元机翼系统的随机颤振。主要由随机系统的二维概率密度和最大Lyapunov指数研究了随机分岔,包括P-分岔和D-分岔,还分析了系统的功率谱密度函数。得到结果如下:当气流流速分别位于颤振前区域和颤振后区域时,随着随机扰动强度的由弱变强,双维概率密度的形状都发生了变化,证明了气流流速在这两种区域都发生了P-分岔。而由系统的最大Lyapunov指数表明不论在弱或强的随机扰动下,也不论气流流速位于哪种区域内,而D-分岔都没有发生。还得到了不同气流流速时的功率谱密度函数曲线,证实了颤振发生时,系统的能量更集中在颤振频率上。

Abstract

The 2-DOF airfoil system with freeplay nonlinearity in pitch, excited by longitudinal and vertical random turbulence, is investigated numerically. The random bifurcation including P-and D-bifurcation is studies in term of the Bi-dimension probability density function (PDF) and the largest Lyapunov exponent respectively. The power spectral density function is also obtained in the paper. The results show in two different aspects. First when the airspeed lies in pre- and post-flutter speeds regime, the shapes of the Bi-dimension PDFs change as the turbulence intensity change from low to high, which demonstrates that the P-bifurcation has happened at the both airspeeds regimes. However, the largest Lyapunov exponents show that the D-bifurcation has not happened in whatever pre- and post-flutter speeds regime regardless when the turbulence intensity is low or high. Second the power spectral density functions are obtained in different airspeed regimes, the conclusion presents that when the airfoil flutter occur, the more power of the system focus on the flutter frequency.

关键词

随机颤振 间隙非线性 随机分岔 最大Lyapunov指数 功率谱密度函数

Key words

random flutter / freeplay nonlinear / random bifurcation / the largest Lyapunov exponent / power spectral density function

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赵德敏;张琪昌;王炜. 具有间隙非线性的二元机翼的随机分岔和功率谱分析 [J]. 振动与冲击, 2009, 28(6): 86-89
ZHAO Demin;ZHANG Qichang;WANG Wei. RANDOM BIFURCATION AND POWER SPECTRUM ANALYSIS OF A 2-DOF AIRFOIL WITH FREEPLAY NONLINEAR IN PITCH[J]. Journal of Vibration and Shock, 2009, 28(6): 86-89
中图分类号: V215.3   

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