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首页> 外文期刊>Aerospace science and technology >Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow
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Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow

机译：超音速流中具有立方非线性的二维机翼的混沌运动

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摘要

Using a combination of analytical and numerical methods, the paper studies chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. While the system is periodic and chaotic alternately as the wing mass static moment about the elastic axis increases. When the nonlinear stiffness coefficient crosses its critical value, the system is always chaotic. Numerical simulations are also given, which confirm the analytical results.%Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing210016, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;Department of Mechanics, Tianjin University, Tianjin 300072, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing210016, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;
机译：结合分析和数值方法，本文研究了超声速流中具有立方非线性的二维机翼的混沌运动。利用不确定系数法，找到了同斜轨道，并证明了同斜轨道级数展开的一致收敛性。分析表明，存在一个将初始平衡点与其自身连接在一起的同斜轨道，因此该系统通过Si'lnikov准则发生了马蹄形马蹄形混沌。该系统通过周期倍增的分叉演变成混沌运动，并且随着无因次气流速度的增加而再次具有周期性。当系统是周期性的且混乱的时，随着机翼质量绕弹性轴的静力矩增加。当非线性刚度系数超过其临界值时，系统始终处于混乱状态。数值模拟也证实了分析结果。南京航空航天大学数学系，南京210016，天津市非线性动力学与混沌控制重点实验室，天津300072；力学部，天津大学，天津300072，天津非线性动力学与混沌控制重点实验室，天津300072;南京航空航天大学数学系，南京210016，天津非线性动力学与混沌控制重点实验室，中国天津300072;

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  • 来源
    《Aerospace science and technology》 |2013年第1期|138-144|共7页
  • 作者

    Liangqiang Zhou; Yushu Chen; Fangqi Chen;

  • 作者单位

    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing210016, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;

    Department of Mechanics, Tianjin University, Tianjin 300072, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;

    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing210016, PR China,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    airfoil; chaotic motion; nonlinearity; si'lnikov criterion;

    机译：翼型;混沌运动非线性西尔尼科夫准则;

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