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1∶2内共振情况下点阵夹芯板动力学的奇异性分析

郭宇红 张伟 杨晓东

郭宇红, 张伟, 杨晓东. 1∶2内共振情况下点阵夹芯板动力学的奇异性分析[J]. 应用数学和力学, 2018, 39(5): 506-528. doi: 10.21656/1000-0887.380190
引用本文: 郭宇红, 张伟, 杨晓东. 1∶2内共振情况下点阵夹芯板动力学的奇异性分析[J]. 应用数学和力学, 2018, 39(5): 506-528. doi: 10.21656/1000-0887.380190
GUO Yuhong, ZHANG Wei, YANG Xiaodong. A Singularity Analysis on Dynamics of Symmetric Cross-Ply Composite Sandwich Plates Under 1∶2 Resonance[J]. Applied Mathematics and Mechanics, 2018, 39(5): 506-528. doi: 10.21656/1000-0887.380190
Citation: GUO Yuhong, ZHANG Wei, YANG Xiaodong. A Singularity Analysis on Dynamics of Symmetric Cross-Ply Composite Sandwich Plates Under 1∶2 Resonance[J]. Applied Mathematics and Mechanics, 2018, 39(5): 506-528. doi: 10.21656/1000-0887.380190

1∶2内共振情况下点阵夹芯板动力学的奇异性分析

doi: 10.21656/1000-0887.380190
基金项目: 国家自然科学基金(11290152;11072008;11272016)
详细信息
    作者简介:

    郭宇红(1978—),男,博士生(E-mail: gst9901@163.com);张伟(1960—),男,教授,博士生导师 (通讯作者. E-mail: sandyzhang0@yahoo.com);杨晓东(1979—),男,教授,博士生导师 (E-mail: jxdyang@163.com).

  • 中图分类号: O322

A Singularity Analysis on Dynamics of Symmetric Cross-Ply Composite Sandwich Plates Under 1∶2 Resonance

Funds: The National Natural Science Foundation of China(11290152;11072008;11272016)
  • 摘要: 内共振是一种典型的非线性动力学行为,点阵夹芯板在航空航天领域中有着广泛的应用背景.研究点阵夹芯板的内共振问题具有重要的理论及工程意义.在横向激励与面内激励联合作用下,基于四边简支点阵夹芯板的动力学方程,利用多尺度法得到极坐标形式的平均方程,进而化简成稳态形式的代数方程,研究其在1∶2内共振情况下的非线性动力学行为.该文利用推广的奇异性理论研究分叉问题,基于稳态形式的代数方程,计算出含有两个调谐参数、一个横向激励和一个面内激励这4个参数的限制切空间;在强等价的条件下,简化了稳态形式的代数方程;在非退化的情况下,计算出简化的代数方程的正规形;对于含有两个状态变量和4个分叉参数的一般非线性动力学方程的奇异性理论进行了推广;利用推广的奇异性理论得到正规形余维4的18个普适开折的表达式;计算出普适开折转迁集的表达式;这样清楚了点阵夹芯板受到小扰动,当分叉、滞后和双极限点产生时,调谐参数和激励参数之间的关系,数值仿真了转迁集和分叉图,结果表明在不同的分叉区域有不同的振动形式.
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出版历程
  • 收稿日期:  2017-07-03
  • 修回日期:  2018-04-11
  • 刊出日期:  2018-05-15

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