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黏弹性屈曲梁非线性内共振稳态周期响应

熊柳杨 张国策 丁虎 陈立群

熊柳杨, 张国策, 丁虎, 陈立群. 黏弹性屈曲梁非线性内共振稳态周期响应[J]. 应用数学和力学, 2014, 35(11): 1188-1196. doi: 10.3879/j.issn.1000-0887.2014.11.002
引用本文: 熊柳杨, 张国策, 丁虎, 陈立群. 黏弹性屈曲梁非线性内共振稳态周期响应[J]. 应用数学和力学, 2014, 35(11): 1188-1196. doi: 10.3879/j.issn.1000-0887.2014.11.002
XIONG Liu-yang, ZHANG Guo-ce, DING Hu, CHEN Li-qun. Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1188-1196. doi: 10.3879/j.issn.1000-0887.2014.11.002
Citation: XIONG Liu-yang, ZHANG Guo-ce, DING Hu, CHEN Li-qun. Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1188-1196. doi: 10.3879/j.issn.1000-0887.2014.11.002

黏弹性屈曲梁非线性内共振稳态周期响应

doi: 10.3879/j.issn.1000-0887.2014.11.002
基金项目: 国家自然科学基金(重点项目)(11232009);国家自然科学基金(11372171;11422214);上海市教委科研创新项目(12YZ028)
详细信息
    作者简介:

    熊柳杨(1991—), 男, 江西宜春人, 硕士生(E-mail: xly0831@126.com);丁虎(1978—), 男,安徽明光人,研究员,博士(通讯作者. E-mail: dinghu3@shu.edu.cn).

  • 中图分类号: O322;O345

Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

Funds: The National Natural Science Foundation of China(Key Program)(11232009); The National Natural Science Foundation of China(11372171;11422214)
  • 摘要: 研究了内共振下简支边界屈曲黏弹性梁受迫振动稳态周期幅频响应.考虑Kelvin黏弹性本构关系,并通过对非平凡平衡位形做坐标变换,建立屈曲梁横向振动的非线性偏微分-积分模型.基于对控制方程的Galerkin截断,得到多维非线性常微分方程组.在前两阶模态内共振存在的条件下,运用多尺度法分析截断后的控制方程,利用可解性条件消除长期项,获得一阶主共振下的幅值与相角方程.通过数值算例以展示系统稳态幅频响应关系以及失稳区域,从而聚焦系统共振中存在的非线性现象,如跳跃现象、滞后现象,并讨论了双跳跃现象随轴向荷载的演化.通过直接数值方法处理截断方程,数值验证近似解析解,计算结果表明多尺度法具有较高精度.
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出版历程
  • 收稿日期:  2014-05-23
  • 刊出日期:  2014-11-18

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