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弹性约束浅拱的非线性动力响应与分岔分析

易壮鹏 张勇 王连华

易壮鹏, 张勇, 王连华. 弹性约束浅拱的非线性动力响应与分岔分析[J]. 应用数学和力学, 2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008
引用本文: 易壮鹏, 张勇, 王连华. 弹性约束浅拱的非线性动力响应与分岔分析[J]. 应用数学和力学, 2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008
YI Zhuang-peng, ZHANG Yong, WANG Lian-hua. Nonlinear Dynamic Response and Bifurcation Analysis of the Elastically Constrained Shallow Arch[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008
Citation: YI Zhuang-peng, ZHANG Yong, WANG Lian-hua. Nonlinear Dynamic Response and Bifurcation Analysis of the Elastically Constrained Shallow Arch[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008

弹性约束浅拱的非线性动力响应与分岔分析

doi: 10.3879/j.issn.1000-0887.2013.11.008
基金项目: 国家自然科学基金资助项目(11002030; 11032004); 教育部新世纪优秀人才支持计划资助项目(NCET-09-0335)
详细信息
    作者简介:

    易壮鹏(1979—),男,湖南长沙人,副教授,博士,硕士生导师(通讯作者. E-mail: yizhuangpeng@163.com).

  • 中图分类号: U311.2; O302

Nonlinear Dynamic Response and Bifurcation Analysis of the Elastically Constrained Shallow Arch

Funds: The National Natural Science Foundation of China(11002030; 11032004); The Program for New Century Excellent Talents in University of China(NCET-09-0335)
  • 摘要: 浅拱采用竖向、转动方向弹性约束时,自振频率和模态与理想的铰支/固结边界存在差异,不同约束刚度将改变外激励下的非线性响应及各种分岔产生的参数域.由浅拱基本假定建立无量纲动力学方程, 采用在频率和模态中考虑约束刚度大小的方法,通过Galerkin全离散和多尺度摄动分析导出极坐标、直角坐标形式的平均方程, 其中方程系数与约束刚度一一对应.用数值方法分析了周期激励下竖向弹性约束系统最低两阶模态之间1∶2内共振时的动力行为, 所得结果与有限元的对比以及平均方程系数的收敛性证明了所采用方法是可行的.随着激励幅值、频率的变化存在若干分岔点,分岔发生时的参数分布与约束刚度值有关,在由分岔点连接的不稳定区或共振区附近,存在一系列稳态解、周期解、准周期解和混沌解窗口,且随参数的变化可观测到倍周期分岔.
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出版历程
  • 收稿日期:  2013-07-05
  • 刊出日期:  2013-11-15

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