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磁场中旋转运动圆环板主共振分岔及混沌研究

朴江民 胡宇达

朴江民, 胡宇达. 磁场中旋转运动圆环板主共振分岔及混沌研究[J]. 应用数学和力学, 2016, 37(11): 1181-1197. doi: 10.21656/1000-0887.370141
引用本文: 朴江民, 胡宇达. 磁场中旋转运动圆环板主共振分岔及混沌研究[J]. 应用数学和力学, 2016, 37(11): 1181-1197. doi: 10.21656/1000-0887.370141
PIAO Jiang-min, HU Yu-da. Principal Resonance Bifurcation and Chaos of Rotating Annular Plates in Magnetic Fields[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1181-1197. doi: 10.21656/1000-0887.370141
Citation: PIAO Jiang-min, HU Yu-da. Principal Resonance Bifurcation and Chaos of Rotating Annular Plates in Magnetic Fields[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1181-1197. doi: 10.21656/1000-0887.370141

磁场中旋转运动圆环板主共振分岔及混沌研究

doi: 10.21656/1000-0887.370141
基金项目: 国家自然科学基金(11472239);河北省自然科学基金(A2015203023);河北省高等学校自然科学研究重点项目(ZD20131055)
详细信息
    作者简介:

    朴江民(1991—),男,硕士(E-mail: yiensoha@163.com);胡宇达(1968—),男,教授,博士,博士生导师(通讯作者. E-mail: huyuda03@163.com).

  • 中图分类号: O322

Principal Resonance Bifurcation and Chaos of Rotating Annular Plates in Magnetic Fields

Funds: The National Natural Science Foundation of China(11472239)
  • 摘要: 研究了磁场中旋转运动圆环板的磁弹性主共振及分岔、混沌问题.通过Hamilton(哈密顿)原理推得磁场中旋转运动圆环板的横向振动方程,并采用Bessel(贝塞尔)函数作为振型函数进行Galerkin(伽辽金)积分,得到磁场中旋转运动圆环板的无量纲非线性振动常微分方程.利用多尺度法展开,得到静态分岔方程、对应的转迁集与分岔图,以及物理参数作为分岔控制参数时的分岔图.利用Mel’nikov(梅利尼科夫)方法,对系统混沌特性进行研究,得到外边夹支内边自由边界条件下异宿轨破裂的条件;通过数值计算,得到外激振力幅值作为分岔控制参数时系统的分岔图与指定参数条件下系统响应图.结果表明,磁场扼制多值现象的产生;激振频率、转速、磁感应强度越小,激振力幅值越大,系统的异宿轨越容易发生破裂,从而引发混沌或概周期运动.
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出版历程
  • 收稿日期:  2016-05-10
  • 修回日期:  2016-06-26
  • 刊出日期:  2016-11-15

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