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含外激励van der Pol-Mathieu方程的非线性动力学特性分析

黄建亮 王腾 陈树辉

黄建亮, 王腾, 陈树辉. 含外激励van der Pol-Mathieu方程的非线性动力学特性分析[J]. 力学学报, 2021, 53(2): 496-510. doi: 10.6052/0459-1879-20-310
引用本文: 黄建亮, 王腾, 陈树辉. 含外激励van der Pol-Mathieu方程的非线性动力学特性分析[J]. 力学学报, 2021, 53(2): 496-510. doi: 10.6052/0459-1879-20-310
Huang Jianliang, Wang Teng, Chen Shuhui. NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 496-510. doi: 10.6052/0459-1879-20-310
Citation: Huang Jianliang, Wang Teng, Chen Shuhui. NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 496-510. doi: 10.6052/0459-1879-20-310

含外激励van der Pol-Mathieu方程的非线性动力学特性分析

doi: 10.6052/0459-1879-20-310
基金项目: 1) 国家自然科学基金资助项目(11972381)
详细信息
    作者简介:

    2) 黄建亮, 教授, 主要研究方向: 非线性动力学与控制. E-mail: huangjl@mail.sysu.edu.cn

    通讯作者:

    黄建亮

  • 中图分类号: O322

NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION

  • 摘要: 本文针对含有自激励, 参数激励和外激励等三种激励联合作用下van der Pol-Mathieu方程的周期响应和准周期运动进行分析, 发现其准周期运动的频谱中含有均匀边频带这一新的特性. 首先, 采用传统的增量谐波平衡法(IHB法)分析了van der Pol-Mathieu方程的周期响应, 得到了其非线性频率响应曲线; 再利用Floquet理论对周期解进行稳定性分析, 得到了两种类型的分岔及它们的位置. 然后, 基于van der Pol-Mathieu方程准周期运动的频谱中边频带相邻频率之间是等距的且含有两个不可约的基频的特性(其中一个基频是已知的, 另一个基频事先是未知的), 推导了相应的两时间尺度IHB法, 精确计算出van der Pol-Mathieu方程的准周期运动的另一个未知基频和所有的频率成份及其对应的幅值, 尤其在临界点附近处的准周期运动响应. 得到的准周期运动结果和利用四阶龙格-库塔(RK)数值法得到的结果高度吻合. 最后, 研究发现了含外激励van der Pol-Mathieu方程在不同激励频率时的一些丰富而有趣的非线性动力学现象.

     

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出版历程
  • 收稿日期:  2020-09-06
  • 刊出日期:  2021-02-10

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