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Chaos in a Magnetic Pendulum Subjected to Tilted Excitation and Parametric Damping

机译：倾斜振动和参数阻尼作用下的磁摆中的混沌

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摘要

The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate the Melnikov predictions. In the absence of parametric damping, the results show that an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly.
机译：研究了倾斜谐波激励和参量阻尼对非对称磁摆混沌动力学的影响。梅尔尼科夫方法用于根据高斯超几何函数得出过渡到非周期性运动的标准。吸引盆地的规则形状和分形形状用于验证梅尔尼科夫的预测。在没有参数阻尼的情况下，结果表明，激励倾斜角的增大会导致混沌域的下界增大，并在激励的垂直位置产生奇异性。还显示出没有周期性波动的参数阻尼的存在可以增强或抑制混沌，而具有周期性波动的参数阻尼可以显着地增加规则运动的区域。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第10期|546364.1-546364.18|共18页
  • 作者

    C. A. Kitio Kwuimy; C. Nataraj; M. Belhaq;

  • 作者单位

    Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova　University, 800 Lancaster Avenue, Villanova, PA 19085, USA;

    Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova　University, 800 Lancaster Avenue, Villanova, PA 19085, USA;

    Laboratory of Mechanics, University Hassan Ⅱ, Casablanca, Morocco;

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