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基础竖向激励下复合材料圆弧拱的面内参数共振失稳研究

刘圆圆 刘爱荣

刘圆圆, 刘爱荣. 基础竖向激励下复合材料圆弧拱的面内参数共振失稳研究[J]. 工程力学, 2022, 39(S): 15-20. doi: 10.6052/j.issn.1000-4750.2021.05.S004
引用本文: 刘圆圆, 刘爱荣. 基础竖向激励下复合材料圆弧拱的面内参数共振失稳研究[J]. 工程力学, 2022, 39(S): 15-20. doi: 10.6052/j.issn.1000-4750.2021.05.S004
LIU Yuan-yuan, LIU Ai-rong. STUDY ON IN-PLANE PARAMETRIC RESONANCE OF COMPOSITE LAMINATED CIRCULAR ARCH UNDER A VERTICAL BASE EXCITATION[J]. Engineering Mechanics, 2022, 39(S): 15-20. doi: 10.6052/j.issn.1000-4750.2021.05.S004
Citation: LIU Yuan-yuan, LIU Ai-rong. STUDY ON IN-PLANE PARAMETRIC RESONANCE OF COMPOSITE LAMINATED CIRCULAR ARCH UNDER A VERTICAL BASE EXCITATION[J]. Engineering Mechanics, 2022, 39(S): 15-20. doi: 10.6052/j.issn.1000-4750.2021.05.S004

基础竖向激励下复合材料圆弧拱的面内参数共振失稳研究

doi: 10.6052/j.issn.1000-4750.2021.05.S004
基金项目: 国家自然科学基金项目(51878188);高等学校学科创新引智计划项目(111计划D21021);广州市科技计划项目(20212200004);中国工程院战略咨询重点项目(2021-XZ-37)
详细信息
    作者简介:

    刘圆圆(1991−),女,河北人,博士生,主要从事新型材料拱的动力稳定研究(E-mail: 2111616069@e.gzhu.edu.cn)

    通讯作者:

    刘爱荣(1972−),女,山西人,教授,博士,博导,主要从事拱的静动力稳定研究(E-mail: liuar@gzhu.edu.cn)

  • 中图分类号: TU311.2

STUDY ON IN-PLANE PARAMETRIC RESONANCE OF COMPOSITE LAMINATED CIRCULAR ARCH UNDER A VERTICAL BASE EXCITATION

  • 摘要: 该文研究了基础竖向激励作用下复合材料圆弧层合拱的平面内参数共振失稳。基于Hamilton原理推导了拱的动力稳定平衡微分方程和Mathieu-Hill方程,获得了层合拱周期2T和周期T对应的动力不稳定域。探明了矢跨比以及铺层角度对动力不稳定域的影响规律。研究结果表明:参数共振主要出现在两倍的结构自振频率附近;随着矢跨比的减小,动力不稳定域的域宽逐渐增大,临界激励频率逐渐增大;同斜交铺层相比,正交铺层拱的动力不稳定域的域宽较小;对于斜交铺层,随着铺层角度增大,动力不稳定域的域宽逐渐增加,临界激振频率向低频方向移动。
  • 图  1  基础竖向激励下两端固接层合拱计算简图

    Figure  1.  A vertically base-excited circular arch with fix-ended support

    图  2  截面示意图

    Figure  2.  Cross-section of the arch

    图  3  铺层角度示意图

    Figure  3.  Ply-angle of the arch

    图  4  一阶反对称周期2T不稳定域

    Figure  4.  First-order antisymmetric period 2T instability region

    图  5  一阶反对称周期T不稳定域

    Figure  5.  First-order antisymmetric period T instability region

    图  6  二阶正对称周期2T不稳定域

    Figure  6.  Second-order symmetric period 2T instability region

    图  7  二阶正对称周期T不稳定域

    Figure  7.  Second-order symmetric period T instability region

    图  8  铺层角对不稳定域的影响

    Figure  8.  The effect of ply angles on instability region

    表  1  复合材料层合拱的物理参数

    Table  1.   Physical parameters of an composite laminated arch

    截面尺寸/m跨径L/m密度ρ/(kg/m3)E1/PaE2/Paν12G12/Pa
    0.002×0.00090.818005.38×10101.79×10100.258.96×109
    注:E1E2分别代表材料在弹性主方向上的横、纵向弹性模量;ν12为材料的横纵泊松比;G12为材料面内剪切模量。
    下载: 导出CSV

    表  2  不同矢跨比条件下[0/90]4铺层拱的圆频率$ {\omega _n} $

    Table  2.   Circular frequency $ {\omega _n} $ of [0/90]4 arches with different rise-span-ratios

    矢跨比一阶频率$ {\omega _{\text{1}}} $误差/(%)二阶频率$ {\omega _{\text{2}}} $误差/(%)
    解析解数值解解析解数值解
    1/582.0683.401.61157.05159.031.25
    1/795.5795.470.10177.16177.460.17
    1/10103.70103.150.53189.29188.820.25
    下载: 导出CSV
  • [1] 李康杰. 圆弧单拱动力稳定性的实验研究[D]. 广州: 广州大学, 2016.

    Li Kangjie. Experimental study on the dynamic stability of circular single arch [D]. Guangzhou: Guangzhou University, 2016. (in Chinese)
    [2] 卢汉文. 圆弧拱平面外稳定性研究[D]. 广州: 广州大学, 2018.

    Lu Hanwen. Research on out-of plane buckling of circular arches [D]. Guangzhou: Guangzhou University, 2018. (in Chinese)
    [3] Zhong Z L, Liu A R, Fu J Y, et al. Analytical and experimental studies on out-of-pane dynamic parametric instability of a circular arch under a vertical harmonic base excitation [J]. Journal of Sound and Vibration, 2021, 500: 116011. doi: 10.1016/j.jsv.2021.116011
    [4] Yang Z C, Liu A R, Pi Y L, et al. Nonlinear dynamic buckling of fixed shallow arches under impact loading: An analytical and experimental study [J]. Journal of Sound and Vibration, 2020, 487: 115622. doi: 10.1016/j.jsv.2020.115622
    [5] Liu A R, Lu H W, Fu J Y, et al. Analytical and experimental studies on out-of-plane dynamic instability of shallow circular arch based on parametric resonance [J]. Nonlinear Dynamics, 2017, 87(1): 677 − 694. doi: 10.1007/s11071-016-3068-7
    [6] Liu A R, Yang Z C, Lu H W, et al. Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance [J]. Journal of Vibration & Control, 2017, 24(19): 4419 − 4432.
    [7] 张紫祥, 刘爱荣, 黄永辉, 等. 集中荷载作用下弹性扭转约束层合浅拱的非线性面内稳定[J]. 工程力学, 2020, 37(增刊): 13 − 19, 31. doi: 10.6052/j.issn.1000-4750.2019.04.S048

    Zhang Zixiang, Liu Airong, Huang Yonghui, et al. Nonlinear in-plane buckling of rotationally restrained shallow laminated arches under a central concentrated load [J]. Engineering Mechanics, 2020, 37(Suppl): 13 − 19, 31. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.04.S048
    [8] 钟子林, 刘爱荣. 携带集中质量的矩形薄板面外非线性动力失稳研究[J]. 工程力学, 2020, 37(增刊): 6 − 12. doi: 10.6052/j.issn.1000-4750.2019.04.S018

    Zhong Zilin, Liu Airong. Study on out-of-plane nonlinear dynamic instability of thin rectangular plate with concentrated mass [J]. Engineering Mechanics, 2020, 37(Suppl): 6 − 12. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.04.S018
    [9] Zhang Z X, Liu A R, Yang J, et al. Nonlinear in-plane buckling of shallow laminated arches incorporating shear deformation under a uniform radial loading [J]. Composite Structures, 2020, 252: 112732. doi: 10.1016/j.compstruct.2020.112732
    [10] Henrych J. The dynamics of arches and frames [M]. New York: Elsevier, 1981: 21 − 24.
    [11] Bolotin V V. The dynamic stability of elastic systems [M]. San Francisco, California: Holden-Day, 1964.
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出版历程
  • 收稿日期:  2021-05-23
  • 修回日期:  2022-03-10
  • 网络出版日期:  2022-04-30
  • 刊出日期:  2022-06-06

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