Parametric vibration model for a viscous damper-cable system considering the effect of additional stiffness
WANG Feng1,LI Chunqing1,LIU Zhangjun2,JIN Xuguang1
1.Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University，Yichang 443002，China；
2.School of Civil Engineering and Architecture，Wuhan Institute of Technology，Wuhan 430074，China
In order to accurately evaluate the control effect of viscous dampers on the parametric vibration of stay cables, the effects of the geometric nonlinearity, inclination and tower-beam synergistic vibration of stay cables were considered and a coupled model for the parametric vibration of the viscous damper-stay cable-tower-beam system was established by introducing an additional stiffness, and the equations of motion of stay cables with viscous dampers were derived.A formula for calculating the damping coefficient of viscous dampers considering the effect of additional stiffness was proposed and the result was compared with that by the traditional single-cable model.The influence of the additional stiffness on the natural frequency and vibration time history of stay cables was analyzed numerically.The influences of the additional stiffness and installation position of viscous dampers on the parametric vibration of stay cables with three typical cable-beam frequency ratios were studied.The results show that the additional stiffness of viscous dampers has great influence on the natural frequency of the cable, but the installation position has little influence on the natural frequency; the greater the additional stiffness, the farther the installation position apart from the anchorage end of cable-girder, the higher the influences; the stiffness of dampers has great influence on the vibration time history of cables, which will accelerate the displacement attenuation of cable; with the increase of additional stiffness, the maximum vibration amplitude tends to decrease, but the amplitude attenuation rate increases first and then tends to be stable.There is an optimal additional stiffness k for the viscous damper-cable-beam system.With the increase of installation position ratio u, the amplitude and amplitude attenuation rate of stay cables show a non-linearly decreasing trend.There exists a critical installation position ratio u.It is suggested that the installation position ratio of dampers should be controlled to below 0.045.
汪峰1，李春清1，刘章军2，金旭光1. 考虑附加刚度的黏滞阻尼器-斜拉索参数振动模型及控制分析[J]. 振动与冲击, 2020, 39(22): 183-191.
WANG Feng1,LI Chunqing1,LIU Zhangjun2,JIN Xuguang1. Parametric vibration model for a viscous damper-cable system considering the effect of additional stiffness. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(22): 183-191.
[1] 梁栋，狄方殿，陈红霞，等. 索-梁耦合振动下的拉索复合减振方法研究[J]. 振动与冲击，2018，37(5)：241-247.
Wu Dong, Di Fangdian，Chen Hongxia, et al. Cable’s compound vibration reduction method under cable-girder coupled vibration[J]. Journal of Vibration and Shock, 2018，37(5)：241-247 (in Chinese)
[2] Lilien J L，Pinto Da Costa A. Vibration amplitudes caused by parametric excitation of cable stayed structures[J]. Journal of Sound and Vibration，1994，174(1)：69-90.
[3] Yamaguchi H, Fujino Y. Stayed cable dynamics and its vibration control [M]. Bridge Aerodynamics, Balkema Rotterdam, the Netherlands，1998：235-253.
[4] 巫生平，张超，房贞政. 斜拉桥粘滞阻尼器设计方案及参数回归分析[J]. 桥梁建设，2014，44(05)：21-26.
Wu Shengping，Zhang Chao，Fang Zhenzheng. Design Schemes and Parameter Regression Analysis of Viscous Dampers for Cable-Stayed Bridge [J]. Bridge Construction，2014，44(05)：21-26 (in Chinese)
[5] 周海俊，丁炜，孙利民. 拉索-阻尼器-弹簧系统的阻尼特性分析[J]. 工程力学，2014，31(01)：79-84.
Zhou Haijun，Ding Wei，Sun Limin. Damping of Taut Cable with a Damper and Spring [J]. Engineering Mechanics，2014，31(01)：79-84 (in Chinese)
[6] 李寿英，王世峰，陈政清. 阻尼器支架刚度对悬索桥吊索减振效果影响的数值研究[J]. 湖南大学学报(自然科学版)，2017，44(01)：9-15.
Li Shouying, Wang Shifeng, Chen Zhengqing. Numerical study on the effect of damping bracket stiffness on suspension cable vibration reduction of suspension bridge[J]. Journal of hunan university (natural science edition)，2017，44(01)：9-15(in Chinese)
[7] 段元锋，李频，周仙通，等. 斜拉索外置式黏滞阻尼器实用设计方法[J]. 中国公路学报，2015，(11): 46-51+59.
Duan Yuanfeng，Li Pin，Zhou Xiantong，et al. Practical Design Method for External Viscous Damper of Stay Cable[J]. China Journal of Highway and Transport，2015，(11)：46-51+59 (in Chinese)
[8] E Caetano，A Cultha，C A Tylor. Investigation of dynamic cable-interaction in a physical model of cable-stayed bridge Part l: modal analysis [J]. Earthquake Engineering and Structural Dynamics，2000，29：484-498.
[9] A Berlioz，C H Lamarque. A nonlinear model of for the dynamics of an inclined cable [J]. Journal of Sound and Vibration，2005，279：619-639
[10] P Wanit Chai, Y Fujino, T. Susurnpow. A nonlinear dynamic model for cables and its application to a cable-structure system [J]. Journal of Sound and Vibration. 1995，187(4)：695-712
[11] 汪峰，陈福清，文晓旭，等. 考虑温度影响的斜拉索参数振动模型及响应分析[J]. 重庆交通大学学报(自然科学版)，2016，35(2)：1-6.
Wang Feng，Chen Fuqing，Wen Xiaoxu，et al. Analysis of Cable Parametric Vibration Model and Response with Consideration of Temperature Effect[J]. Journal of Chong qing Jiao tong University (Natural Science)，2016，35(2)：1-6 (in Chinese)
[12] 汪峰，文晓旭，刘章军. 斜拉桥塔-索-梁耦合参数振动模型及响应分析[J]. 固体力学学报，2015，36(5): 446-452.
Wang Feng, Wen Xiaoxu, Liu Zhangjun. Coupled vibration model for Tower-cable-deck of long-span Cable-stayed bridge and its response analysis [J]. Chinese Journal of Solid Mechanics, 2015, 36(5): 446-452 (in Chinese)
[13] 杨咏漪, 陈克坚. 大跨度铁路斜拉桥斜拉索参数振动分析[J]. 铁道工程学报，2012，169(10)：60-65.
Yang Yongyi, Chen Kejian. Research on parametric oscillation of cables for long span railway cable-stayed bridge [J]. Journal of Railway Engineering Society，2012，169(10)：60-65(in Chinese)
[14] 康厚军，赵跃宇，蒋丽忠. 参数振动和强迫振动激励下超长拉索的面内非线性振动[J]. 中南大学学报(自然科学版)，2011，42(8)：2439-2445.
Kang Houjun，Zhao Yueyu，Jiang Lizhong. In-plane Nonlinear Vibration of Super Long Stay Cables under Parametric and Forcied Excitations [J]. Journal of Central South University (Science and Technology), 2011，42(8): 2439-2445(in Chinese)
[15] 张妍. 斜拉桥塔-索-面耦合模型的内共振分析及其控制研究[D].南京：南京航空航天大学，2010.
Zhang Yan. Internal resonance analysis and control of the pylon-cable-surface coupling model of cable-stayed Bridges [D]. Nanjing：Nanjing university of aeronautics and astronautics，2010(in Chinese)
[16] Gattulli V，Martinelli L，Perotti F，etal. Nonlinear oscillations of cables under harmonic loading using analytical and finite element models[J]. Computer Methods in Applied Mechanics and Engineering，2004，193(1/2): 69−85.
[17] Pacheco B M，Fujino Y，Sulekh A. Estimation curve for modal damping in stay cables with viscous damper [J]. Journal of Structural Engineering，1993，119(6)：1961-1978.
[18] 赵国辉，高建华，刘健新，等. 悬索桥线性液体黏滞阻尼器阻尼系数优化[J]. 交通运输工程学报，2013，13(3)：33-39.
Zhao Guohui，Gao Jianhua，Liu Jianxin，et al. Damping coefficient optimization of linear fluid viscous damper for suspension bridge[J].Journal of Traffic and Transportation Engineering，2013，13(3)：33-39(in Chinese)
[19] Q. Wu，K. Takahashi，S. Nakamura. Non-linear response of cables subjected to periodic support excitation considering cable loosening [J]. Journal of Sound and Vibration，2004，27(1/2): 453-463.
[20] 宋力勋. 基于粘滞阻尼器的斜拉桥减震研究[D]. 北京：北京交通大学，2012.
Song Lixun. Research on shock absorption of cable-stayed Bridges based on viscous dampers[D]. Beijing：Beijing jiaotong university，2012 (in Chinese)
[21] 詹英杰. 斜拉索-阻尼器系统振动控制数值分析及试验研究[D].西南交通大学，2016.
Zhan Yingjie. Numerical analysis and experimental research on vibration control of cable-damper system [D]. Southwest Jiaotong University，2016.
