Chaos characteristics of wind-induced vibrations for bridge
Article Text (Baidu Translation)
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摘要: 利用非线性理论和混沌时间序列分析方法, 建立了桥梁风致振动的数学模型, 开发了计算桥梁振动加速度时间序列Lyapunov指数的MATLAB程序, 进行了桥梁涡振和颤振的风洞试验, 分析了不同风攻角下的桥梁风致振动的阻尼比、Lyapunov指数与风速的关系以及涡振振幅与风速的关系, 研究了桥梁颤振和涡振的混沌特性。试验结果表明: 在颤振试验中, 当风速小于颤振临界风速15.5m·s-1时, Lyapunov指数小于0, Lyapunov指数与阻尼比存在很大的相关性, 当风速从3m·s-1增大为18m·s-1时, 相空间逐渐发散; 在涡振试验中, 当风速从4.5m·s-1增大至8.5m·s-1时, Lyapunov指数大于0, 桥梁发生明显涡振, 并由多频振动逐渐转变为单频振动, 相空间变为一个较为理想的圆。桥梁的涡振与颤振均属于混沌现象, 低风速下的Lyapunov指数可用来预测高风速下的风致振动, 并且利用相空间也能识别涡振与颤振。Abstract: According to nonlinear theory and chaotic time series analysis method, the mathematical model of bridge wind-induced vibration was built.The MATLAB program for calculating the Lyapunov exponent of bridge vibration acceleration time series was developed, and the flutter and vortex vibration were tested in wind tunnel.Under various wind attack angles, the damping ratios of bridge wind-induced vibrations, the relationships between Lyapunov exponents and wind speeds, and the relationships between vortex vibration amplitudes and wind speeds were analyzed, and the chaos characteristics of flutter and vortex vibration were studied.Test result indicates when wind speed is less than critical wind speed (15.5 m·s-1), the Lyapunov exponent is negative in flutter test, and the close correlation between Lyapunov exponent and damping ratio is found.When wind speed increases from 3 m·s-1 to 18 m·s-1, the phase space becomes divergent gradually.In vortex vibration test, when wind speed increases from 4.5 m·s-1 to 8.5 m·s-1, the Lyapunov exponent is more than 0, obvious vortex vibration happens, and multi-frequency vibration turns to single frequency vibration gradually.The phase space also becomes an ideal circle.Both flutter and vortex vibration are chaos phenomena.Lyapunov exponent at low wind speed can be used to predict the wind-induced vibrations at high windspeed, and the phase space can also be used to explain flutter and vortex vibration.
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[1] 项海帆. 进入21世纪的桥梁风工程研究[J]. 同济大学学报: 自然科学版, 2002, 30 (5): 529-532. doi: 10.3321/j.issn:0253-374X.2002.05.001XIANG Hai-fan. Study on bridge wind engineering into 21st century[J]. Journal of Tongji University: Natural Science, 2002, 30 (5): 529-532. (in Chinese). doi: 10.3321/j.issn:0253-374X.2002.05.001 [2] OMENZETTER P. Sensitivity analysis of the eigenvalue problem for general dynamic systems with application to bridge deck flutter[J]. Journal of Engineering Mechanics, 2012, 138 (6): 675-682. doi: 10.1061/(ASCE)EM.1943-7889.0000377 [3] NIETO F. An analytical approach to sensitivity analysis of the flutter speed in bridges considering variable deck mass[J]. Advances in Engineering Software, 2011, 42 (4): 117-129. doi: 10.1016/j.advengsoft.2010.12.003 [4] ARGENTINI T, PAGANI A, ROCCHI D, et al. Monte Carlo analysis of total damping and flutter speed of a long span bridge: effects of structural and aerodynamic uncertainties[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2014, 128 (2): 90-104. [5] BRUSIANI F. On the evaluation of bridge deck flutter derivatives using RANS turbulence models[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2013, 119 (1): 39-47. [6] 郭增伟, 葛耀君, 杨詠昕. 基于状态空间的桥梁颤振分析[J]. 华中科技大学学报: 自然科学版, 2012, 40 (11): 27-32. https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201211005.htmGUO Zeng-wei, GE Yao-jun, YANG Yong-xin. Flutter analysis of bridge based on state-space approach[J]. Journal of Huazhong University of Science and Technology: Nature Science Edition, 2012, 40 (11): 27-32. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201211005.htm [7] 辛大波, 欧进萍, 李惠, 等. 基于定常吸气方式的大跨桥梁风致颤振抑制方法[J]. 吉林大学学报: 工学版, 2011, 41 (5): 1273-1278. https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201105016.htmXIN Da-bo, OU Jin-ping, LI Hui, et al. Suppression method for wind-induced flutter of long-span bridge based on steady air-suction[J]. Journal of Jilin University: Engineering and Technology Edition, 2011, 41 (5): 1273-1278. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201105016.htm [8] CASALOTTI A, ARENA A, LACARBONARA W. Mitigation of post-flutter oscillations in suspension bridges by hysteretic tuned mass dampers[J]. Engineering Structures, 2014, 69 (2): 62-71. [9] 许福友, 林志兴, 李永宁, 等. 气动措施抑制桥梁涡振机理研究[J]. 振动与冲击, 2010, 29 (1): 73-76. doi: 10.3969/j.issn.1000-3835.2010.01.016XU Fu-you, LIN Zhi-xing, LI Yong-ning, et al. Research on vortex resonance depression mechanism of bridge deck with aerodynamic measures[J]. Journal of Vibration and Shock, 2010, 29 (1): 73-76. (in Chinese). doi: 10.3969/j.issn.1000-3835.2010.01.016 [10] PATIL A. Mitigation of vortex-induced vibrations in bridges under conflicting objectives[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2011, 99 (12): 1243-1252. doi: 10.1016/j.jweia.2011.10.001 [11] 李清都, 杨晓松. 基于拓扑马蹄的混沌动力学研究进展[J]. 动力学与控制学报, 2012, 10 (4): 293-298. https://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201204005.htmLI Qing-du, YANG Xiao-song. Progresses on chaotic dynamics study with topological horseshoes[J]. Journal of Dynamics and Control, 2012, 10 (4): 293-298. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201204005.htm [12] 何四祥. 混沌在结构工程中的应用研究[D]. 上海: 同济大学, 2007.HE Si-xiang. Chaos in the application of structural engineering research[D]. Shanghai: Tongji University, 2007. (in Chinese). [13] HU Gao-ge, GAO She-sheng, GAO Bing-bing. Chaos control in Cournot-Puu model[J]. Applied Mechanics and Materials, 2014, 494 (1): 1189-1194. [14] POIREL D, PRICE S J. Random binary (coalescence) flutter of a two-dimensional linear airfoil[J]. Journal of Fluids and Structures, 2003, 18 (1): 23-42. doi: 10.1016/S0889-9746(03)00074-4 [15] 余宏波. 斜拉桥拉索风雨激振混沌特性应用研究[D]. 西安: 长安大学, 2012.YU Hong-bo. Application research on chaotic characteristics of wind-rain induced vibration of cables for the cable-stayed bridges[D]. Xi'an: Chang'an University, 2012. (in Chinese). [16] CARACOGLIA L. An Euler-Monte Carlo algorithm assessing Moment Lyapunov Exponents for stochastic bridge flutter predictions[J]. Computers and Structures, 2013, 122 (1): 65-77. [17] 张文胜, 崔志伟. 铁路客运专线特大桥沉降预测模型[J]. 交通运输工程学报, 2011, 11 (6): 31-36. http://transport.chd.edu.cn/article/id/201106005ZHANG Wen-sheng, CUI Zhi-wei. Settlement prediction model of super large bridge for passenger dedicated railway[J]. Journal of Traffic and Transportation Engineering, 2011, 11 (6): 31-36. (in Chinese). http://transport.chd.edu.cn/article/id/201106005 [18] 李国辉, 周世平, 徐得名. 时间序列最大Lyapunov指数的计算[J]. 应用科学学报, 2003, 21 (2): 127-131. doi: 10.3969/j.issn.0255-8297.2003.02.004LI Guo-hui, ZHOU Shi-ping, XU De-ming. Computing the largest Lyapunov exponent from time series[J]. Journal of Applied Sciences, 2003, 21 (2): 127-131. (in Chinese). doi: 10.3969/j.issn.0255-8297.2003.02.004 [19] 郭增伟, 葛耀君. 桥梁自激力脉冲响应函数及颤振时域分析[J]. 中国公路学报, 2013, 26 (6): 103-109. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201306018.htmGUO Zeng-wei, GE Yao-jun. Impulse response functions of self-excited force and flutter analysis in time domain for bridge[J]. China Journal of Highway and Transport, 2013, 26 (6): 103-109. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201306018.htm [20] 管青海, 李加武, 刘建新. 典型箱梁断面双竖向涡振区的成因分析[J]. 长安大学学报: 自然科学版, 2013, 33 (4): 40-46. doi: 10.3969/j.issn.1671-8879.2013.04.008GUAN Qing-hai, LI Jia-wu, LIU Jian-xin. Investigation into formation of two lock-in districts of vertical vortex-induced vibration of a box bridge deck section[J]. Journal of Chang'an University: Natural Science Edition, 2013, 33 (4): 40-46. (in Chinese). doi: 10.3969/j.issn.1671-8879.2013.04.008 [21] 许伦辉, 刘邦明. 城市交通信号控制与仿真[J]. 公路交通科技, 2013, 30 (9): 109-115. https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201309017.htmXU Lun-hui, LIU Bang-ming. Urban traffic signal control and simulation[J]. Journal of Highway and Transportation Research and Development, 2013, 30 (9): 109-115. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201309017.htm [22] 胡庆安, 乔云强, 刘建新. MSS62.5移动模架造桥机风洞试验及抗风分析[J]. 筑路机械与施工机械化, 2006, 23 (10): 36-38. doi: 10.3969/j.issn.1000-033X.2006.10.017HU Qing-an, QIAO Yun-qiang, LIU Jian-xin. Wind tunnel test and anti-wind analysis for MSS62.5[J]. Road Machinery and Construction Mechanization, 2006, 23 (10): 36-38. (in Chinese). doi: 10.3969/j.issn.1000-033X.2006.10.017 [23] LIU Xiao-gang, FAN Jian-sheng, NIE Jian-guo, et al. Behavior of composite rigid frame bridge under bi-directional seismic excitations[J]. Journal of Traffic and Transportation Engineering: English Edition, 2014, 1 (1): 62-71. doi: 10.1016/S2095-7564(15)30090-8 [24] FU Mei-zhen, LIU Yong-jian, LI Na, et al. Application of modern timber structure in short and medium span bridges in China[J]. Journal of Traffic and Transportation Engineering: English Edition, 2014, 1 (1): 72-80. doi: 10.1016/S2095-7564(15)30091-X -