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受损悬索对称性破缺下非线性耦合振动研究

赵珧冰 郑攀攀 陈林聪 康厚军

赵珧冰, 郑攀攀, 陈林聪, 康厚军. 受损悬索对称性破缺下非线性耦合振动研究. 力学学报, 2022, 54(2): 1-11 doi: 10.6052/0459-1879-21-542
引用本文: 赵珧冰, 郑攀攀, 陈林聪, 康厚军. 受损悬索对称性破缺下非线性耦合振动研究. 力学学报, 2022, 54(2): 1-11 doi: 10.6052/0459-1879-21-542
Zhao Yaobing, Zheng Panpan, Chen Lincong, Kang Houjun. Study on nonlinear coupled vibrations of damaged suspended cables with symmetry-breaking. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 1-11 doi: 10.6052/0459-1879-21-542
Citation: Zhao Yaobing, Zheng Panpan, Chen Lincong, Kang Houjun. Study on nonlinear coupled vibrations of damaged suspended cables with symmetry-breaking. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 1-11 doi: 10.6052/0459-1879-21-542

受损悬索对称性破缺下非线性耦合振动研究

doi: 10.6052/0459-1879-21-542
基金项目: 国家自然科学基金资助项目(12072218, 11972151)
详细信息
    作者简介:

    赵珧冰, 副教授, 主要研究方向: 结构振动与控制. E-mail: ybzhao@hqu.edu.cn

    康厚军, 教授, 主要研究方向: 非线性振动与控制. E-mail: houjun_kang@163.com

  • 中图分类号: O323

STUDY ON NONLINEAR COUPLED VIBRATIONS OF DAMAGED SUSPENDED CABLES WITH SYMMETRY-BREAKING

  • 摘要: 对称性是振动理论中5大美学特征之一, 然而对称性破缺又难以避免. 本文以工程中常见的易损结构—悬索为例, 探究当该系统遭遇非对称性损伤时, 对称性破缺对其面内耦合振动特性影响. 首先建立受损悬索面内非线性动力学模型, 并采用Galerkin法得到离散的无穷维微分方程. 利用多尺度法计算该非线性系统发生面内耦合共振响应的调谐方程. 截取前9阶模态, 利用数值计算方法得到无损和受损悬索的各类共振曲线及其稳定性, 通过计算最大李雅普诺夫指数来确定系统的混沌运动. 研究结果表明: 已有研究常采用抛物线模拟悬索静态构形, 然而一旦发生不对称损伤, 采用分段函数更能准确描述悬索受损后的静态构形; 对称性破缺会导致悬索固有频率之间的交点变为转向点, 其正、反对称模态均变为非对称模态; 受损后悬索的非线性相互作用系数会发生显著改变, 其内共振响应会产生明显变化; 当激励直接作用在高阶模态时, 无损系统会呈现出单模态解和内共振解, 而受损系统并没有呈现出明显的单模态解; 受损系统的分岔和混沌特性会发生改变, 系统将通过倍周期分岔产生混沌运动.

     

  • 图  1  受损悬索构形及特性

    Figure  1.  Configurations and characteristics of the damaged suspended cable

    图  2  悬索模态频率和Irvine参数关系曲线及其模态振型

    Figure  2.  Relationship curves between Irvine parameter and mode frequencies and shapes

    图  3  激励响应幅值曲线 (f1 = 0, σ1 = 0.05和σ2 = 0.2)

    Figure  3.  Excitation response amplitude curves when f1 = 0, σ1 = 0.05 and σ2 = 0.2

    图  4  幅频响应曲线 (f1 = 0, f2 = 0.002和σ2 = 0.2)

    Figure  4.  Frequency-response curves when f1 = 0, f2 = 0.002 and σ2 = 0.2

    图  5  受损悬索霍普夫分岔点附近的动态解 (f1=0, f2=0.002和σ2=0.2)

    Figure  5.  Damaged suspended cable’s dynamic solutions around two Hopf bifurcations when f1=0, f2=0.002 and σ2=0.2

    图  6  PD1附近的相位图: 从周期解到混沌 (1→2→4→8→…→混沌)

    Figure  6.  Phase portraits diagrams around PD1: from periodic motions to chaotic motions (1→2→4→8→…→chaos)

    图  7  时程曲线、相位图、频谱以及庞加莱截面(f1=0, f2=0.002, σ1=0.02772, σ2=0.2)

    Figure  7.  Time history curves, phase portraits, frequency spectrums and Poincare sections when f1=0, f2=0.002, σ1=0.02772, σ2=0.2

    表  1  无损和受损悬索的参数与非线性相互作用系数

    Table  1.   Parameters and nonlinear interaction coefficients of undamaged and damaged suspended cables

    Cable typesmnλ2ωmωnKmmKnnKmn/ KnmK1K2K3
    undamaged1240.3736.26406.2830−265000013290002079000001368000
    damaged1241.8296.15356.15381091850902357−23657809385981024960−1028280
    下载: 导出CSV
  • [1] 胡海岩. 对振动学及其发展的美学思考. 振动工程学报, 2000, 13(2): 161-169 (Hu Haiyan. Aesthetical consideration for vibration theory and its development. Journal of Vibration Engineering, 2000, 13(2): 161-169 (in Chinese) doi: 10.3969/j.issn.1004-4523.2000.02.001
    [2] 胡海岩. 振动力学−研究性教程. 北京: 科学出版社

    Hu Haiyan. Mechanics of Vibration—Research Course. Beijing: Science Press, 2020 (in Chinese)
    [3] 张登博, 唐有绮, 陈立群. 非齐次边界条件下轴向运动梁的非线性振动. 力学学报, 2019, 51(1): 218-227 (Zhang Dengbo, Tang Youqi, Chen Liqun. Nonlinear vibrations of axially moving beams with nonhomogeneous boundary conditions. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 218-227 (in Chinese) doi: 10.6052/0459-1879-18-189
    [4] 康厚军, 郭铁丁, 赵跃宇等. 大跨度斜拉桥非线性振动模型与理论研究进展. 力学学报, 2016, 48(3): 519-535 (Kang Houjun, Guo Tieding, Zhao Yueyu, et al. Review on nonlinear vibration and modeling of large span cable-stayed bridge. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 519-535 (in Chinese) doi: 10.6052/0459-1879-15-436
    [5] Triantafyllou MS, Grinfogel L. Natural frequencies and modes of inclined cables. Journal of Structural Engineering, 1986, 112(1): 139-148 doi: 10.1061/(ASCE)0733-9445(1986)112:1(139)
    [6] Cheng SP, Perkins NC. Closed form vibration analysis of sagged cable/mass suspensions. Journal of Applied Mechanics, 1992, 59(4): 923-928 doi: 10.1115/1.2894062
    [7] Lepidi M, Gattulli V, Vestroni F. Static and dynamic response of elastic suspended cables with damage. International Journal of Solids and Structures, 2007, 44: 8194-8212 doi: 10.1016/j.ijsolstr.2007.06.009
    [8] Wu QX, Takahashi K, Nakamura S. Formulae for frequencies and modes of in-plane vibrations of small-sag inclined cables. Journal of Sound and Vibration, 2005, 279(3-5): 1155-1169 doi: 10.1016/j.jsv.2004.01.004
    [9] 任伟新, 陈刚. 由基频计算拉索拉力的实用公式. 土木工程学报, 2005, 38(11): 26-31 (Ren Weixin, Chen Gang. Practical formulas to determine cable tension by using cable fundamental frequency. China Civil Engineering Journal, 2005, 38(11): 26-31 (in Chinese) doi: 10.3321/j.issn:1000-131X.2005.11.005
    [10] 吴庆雄, 陈宝春. 塔桅结构的斜索面内固有振动计算的修正Irvine方程. 工程力学, 2007, 24(4): 18-23 (Wu Qingxiong, Chen Baochun. Modified Irvine equations for in-plane natural vibrations of inclined cables in tower and guyed mast structures. Engineering Mechanics, 2007, 24(4): 18-23 (in Chinese) doi: 10.3969/j.issn.1000-4750.2007.04.004
    [11] Irvine HM. Cable Structures. Cambridge: MIT Press, 1981
    [12] Srinil N, Rega G, Chucheepsakul S. Large amplitude three-dimensional free vibrations of inclined sagged elastic cables. Nonlinear Dynamics, 2003, 33(2): 129-154 doi: 10.1023/A:1026019222997
    [13] 王浩宇, 吴勇军. 1: 1内共振对随机振动系统可靠性的影响. 力学学报, 2015, 47(5): 807-813 (Wang Haoyu, Wu Yongjun. The influence of one-to-one internal resonance on reliability of random vibration system. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 807-813 (in Chinese) doi: 10.6052/0459-1879-15-058
    [14] 吕敬, 李俊峰, 王天舒等. 充液挠性航天器俯仰运动1: 1: 1内共振动力学分析. 力学学报, 2007, 39(6): 804-812 (Lü Jing, Li Junfeng, Wang Tianshu, et al. Analytical study on 1: 1: 1 internal resonance nonlinear dynamics of a liquid-filled spacecraft with elastic appendages. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(6): 804-812 (in Chinese) doi: 10.3321/j.issn:0459-1879.2007.06.012
    [15] 叶敏, 吕敬, 丁千等. 复合材料层合板1: 1参数共振的分岔研究. 力学学报, 2004, 36(1): 64-71 (Ye Min, Lü Jing, Ding Qian, et al. The bifurcation analysis of the laminated composite plate with 1: 1 parametrically resonance. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(1): 64-71 (in Chinese) doi: 10.3321/j.issn:0459-1879.2004.01.010
    [16] 姜盼, 郭翔鹰, 张伟. 石墨烯三相复合材料板的非线性动力学研究. 动力学与控制学报, 2019, 17(3): 270-280 (Jiang Pan, Guo Xiangying, Zhang Wei. Nonlinear dynamics of a three-phase composite materials plate with grapheme. Journal of Dynamics and Control, 2019, 17(3): 270-280 (in Chinese) doi: 10.6052/1672-6553-2019-021
    [17] 孙莹, 张伟. 1: 1内共振环形桁架天线的稳定性分析. 动力学与控制学报, 2018, 16(3): 281-288 (Sun Ying, Zhang Wei. Analysis on stability of circular mesh antenna with 1: 1 internal resonance. Journal of Dynamics and Control, 2018, 16(3): 281-288 (in Chinese) doi: 10.6052/1672-6553-2018-024
    [18] Srinil N, Rega G. The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. International Journal of Non-Linear Mechanics, 2007, 42(1): 180-195 doi: 10.1016/j.ijnonlinmec.2006.09.005
    [19] Rega G, Srinil N. Nonlinear hybrid-mode resonant forced oscillations of sagged inclined cables at avoidances. Journal of Computational and Nonlinear Dynamics, 2007, 2(4): 324-336 doi: 10.1115/1.2756064
    [20] Chen Z, Chen H, Liu H, et al. Corrosion behavior of different cables of large-span building structures in different environments. Journal of Materials in Civil Engineering, 2020, 32(11): 04020345 doi: 10.1061/(ASCE)MT.1943-5533.0003428
    [21] Chen A, Yang YY, Ma RJ, et al. Experimental study of corrosion effects on high-strength steel wires considering strain influence. Construction and Building Materials, 2020, 240: 117910 doi: 10.1016/j.conbuildmat.2019.117910
    [22] Wang Y, Zheng YQ, Zhang WH, et al. Analysis on damage evolution and corrosion fatigue performance of high strength steel wire for bridge cable: Experiments and numerical simulation. Theoretical and Applied Fracture Mechanics, 2020, 107: 102571 doi: 10.1016/j.tafmec.2020.102571
    [23] Jiang C, Wu C, Cai CS, et al. Corrosion fatigue analysis of stay cables under combined loads of random traffic and wind. Engineering Structures, 2020, 206: 110153 doi: 10.1016/j.engstruct.2019.110153
    [24] Bouaanani N. Numerical investigation of the modal sensitivity of suspended cables with localized damage. Journal of Sound and Vibration, 2006, 292(3-5): 1015-1030 doi: 10.1016/j.jsv.2005.09.013
    [25] Lepidi M. Damage identification in elastic suspended cables through frequency measurement. Journal of Vibration and Control, 2009, 15(6): 867-896 doi: 10.1177/1077546308096107
    [26] Sun HH, Xu J, Chen WZ, et al. Time-dependent effect of corrosion on the mechanical characteristics of stay cable. Journal of Bridge Engineering, 2018, 23(5): 04018019 doi: 10.1061/(ASCE)BE.1943-5592.0001229
    [27] Xu J, Sun HH, Cai SY. Effect of symmetrical broken wires damage on mechanical characteristics of stay cable. Journal of Sound and Vibration, 2019, 461: 114920 doi: 10.1016/j.jsv.2019.114920
    [28] 王立彬, 王达, 吴勇. 损伤拉索的等效弹性模量及其参数分析. 计算力学学报, 2015, 32(3): 339-345 (Wang Libin, Wang Da, Wu Yong. The equivalent elastic modulus of damaged cables and parameter analysis. Chinese Journal of Computational Mechanics, 2015, 32(3): 339-345 (in Chinese) doi: 10.7511/jslx201503007
    [29] 兰成明, 李惠, 鞠杨. 平行钢丝拉索承载力评定. 土木工程学报, 2013, 46(5): 31-38 (Lan Chengming, Li Hui, Ju Yang. Bearing capacity assessment for parallel wire cables. China Civil Engineering Journal, 2013, 46(5): 31-38 (in Chinese)
    [30] Zhu J, Ye GR, Xiang YQ, et al. Dynamic behavior of cable-stayed beam with localized damage. Journal of Vibration and Control, 2011, 17(7): 1080-1089 doi: 10.1177/1077546310378028
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  • 收稿日期:  2021-10-25
  • 录用日期:  2021-12-14
  • 网络出版日期:  2021-12-15

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