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导电薄板的磁弹性组合共振分析

胡宇达 李晶

胡宇达, 李晶. 导电薄板的磁弹性组合共振分析[J]. 应用数学和力学, 2008, 29(8): 954-966.
引用本文: 胡宇达, 李晶. 导电薄板的磁弹性组合共振分析[J]. 应用数学和力学, 2008, 29(8): 954-966.
HU Yu-da, LI Jing. Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate[J]. Applied Mathematics and Mechanics, 2008, 29(8): 954-966.
Citation: HU Yu-da, LI Jing. Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate[J]. Applied Mathematics and Mechanics, 2008, 29(8): 954-966.

导电薄板的磁弹性组合共振分析

详细信息
    作者简介:

    胡宇达(1968- ),男,黑龙江人,教授,博士(联系人.Tel:+86-335-8074576;E-mail:huyuda03@163.com).

  • 中图分类号: O322:O442

Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate

  • 摘要: 基于Mexwell方程,给出了导电薄板的非线性磁弹性振动方程、电动力学方程和电磁力表达式.在此基础上,研究了横向磁场中梁式导电薄板的磁弹性组合共振问题,应用Galerkin法导出了相应的非线性振动微分方程组.利用多尺度法进行求解,得到了系统稳态运动下的幅频响应方程,分析了组合共振激发的条件.根据Liapunov近似稳定性理论,对稳态解的稳定性进行了分析,得到了稳定性的判定条件.通过数值计算,给出了一、二阶模态下共振振幅随调谐参数、激励幅值和磁场强度的变化规律曲线图,以及系统振动的时程响应图、相图、Poincaré映射图和频谱图,进一步分析了电磁、机械等参量对解的稳定性及分岔特性的影响,并讨论了系统的倍周期和概周期等复杂动力学行为.
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出版历程
  • 收稿日期:  2007-09-04
  • 修回日期:  2008-07-15
  • 刊出日期:  2008-08-15

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