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

Zhao Yaobing; Zheng Panpan; Chen Lincong; Kang Houjun

doi:10.6052/0459-1879-21-542

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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

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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

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

doi: 10.6052/0459-1879-21-542

*.
College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian, China
†.
Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Xiamen 361021, Fujian, China
**.
Scientific Research Center of Engineering Mechanics, Guangxi University, Nanning 530004, China

Received Date: 2021-10-25
Accepted Date: 2021-12-14

Available Online: 2021-12-15

Abstract

Abstract

Symmetry is one of the five aesthetic characteristics in the vibration theory, but the symmetry-breaking is also inevitable. This paper takes a common vulnerable structure in engineering-the suspended cable-as an example, and the influences of symmetry-breaking on the planar coupled vibrations have been investigated when the asymmetric damage is occurred. Firstly, the in-plane nonlinear dynamical model of damaged suspended cable has been established, and the nonlinear infinite dimensional differential equations have been obtained by using the Galerkin method. The method of multiple scales has been adopted to obtain the modulation equations of the nonlinear systems’ in-plane coupled vibrations. The resonant curves of undamaged and damaged suspended cables including the first nine modes have been obtained by using the numerical methods, and the stabilities of solutions have also been determined. The largest Lyapunov exponent has been calculated to determine the system’s chaotic motions. The numerical results show that the classical parabolic curves have been often adopted to simulate the suspended cables’ static configurations. However, when the asymmetric damage occurs, the piecewise functions should be used to accurately describe the damaged cables’ static configurations. The symmetry-breaking causes crossover points between two natural frequencies of suspended cables to turn into veering points, and the symmetric/anti-symmetric mode shapes before damage are changed into the asymmetric ones after damaged. The nonlinear interaction coefficients are changed significantly, resulting in significant changes in internal resonant responses. When the excitation is directly applied to the higher-order modes, the single-mode solutions and internal resonant ones are obvious in the undamaged system, while the damaged system does not present the obvious single-mode solutions. The bifurcations and chaos of the damaged system are also changed obviously, and some chaotic motions around the period-doubling bifurcation are observed as to the damaged system.
- damaged suspended cable,
- symmetry-breaking,
- frequency veering,
- coupled resonant responses,
- bifurcation and chaos

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References(30)

References

[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