人群激励下人行桥非线性横向参数振动研究  

Footbridge nonlinear lateral parametric vibration under crowd excitation

作　　者：陈舟 颜全胜[3] 邓德员[4] 陈玉骥 贾布裕 余晓琳[3] CHEN Zhou;VAN Quansheng;DENG Deyuan;CHEN Yuji;JIA Buyu;YU Xiaolin(School of Transportation and Civil Engineering ＆ Architecture,Foshan University-,Foshan 528000,China;College of Civil Engineering ＆ Architecture,China Three Gorges University,Yichang 443002,China;School of Civil Engineering and Transportion,South China University of Technology-,Guangzhou 510640,China;China Construction Steel Structure Co.,Ltd.,Guangzhou 510000,China)

机构地区：[1]佛山科学技术学院交通与土木建筑学院,广东佛山528000 [2]三峡大学土木与建筑学院,湖北宜昌443002 [3]华南理工大学土木与交通学院,广州510640 [4]中建钢构有限公司,广州510000

出　　处：《振动与冲击》2018年第21期46-51,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51208208);中央高校基本科研业务费专项资金资助(2014ZZ0019);宜昌市科技研究与开发项目(A16-302-A07);佛山科学技术学院博士科研启动基金(GG040930)

摘　　要：随着人行桥的跨径越来越大及其结构日渐轻柔,人群行走往往会引起桥梁大幅横向振动问题,考虑大位移引起的几何非线性的影响,针对基频较低的人行桥,建立了基于力与速度之间关系的非线性横向参数振动模型,以伦敦千禧桥为例,用Galerkin方法和多尺度法,对行人引起人行桥参数振动作用下的大幅振动进行了理论和数值分析。临界人数的理论计算值与现有研究成果进行比较,表明该方法可用于不同人行桥的临界人数进行预测,且计算简单方便,说明建立的模型是合理的、正确的;行走频率越接近2倍固有频率能够激起大幅振动所需要的行人数越少,只要轻微的激励,人行桥也会发生大幅振动;考虑非线性振动时,当行人数超过临界人数时,振动幅值趋于稳定的等幅振动,而线性振动时发散振动的非等幅振动;单位时间上桥人数、桥梁的单位长度质量、阻尼、初始条件对人致参数振动响应幅值有不同程度的影响。With increase in span and structural flexibility of a footbridge,walking crowd may cause its large amplitude transverse vibration. Here,considering effects of geometric nonlinearity due to large displacements,aiming at a footbridge with lower fundamental natural frequency,its nonlinear transverse vibration model was built based on the relation between force and velocity. Millennium Bridge in London was taken as an example,and Galerkin method and the multi-scale method were used to do theoretical and numerical analysis for its large amplitude crowd-induced transverse parametric vibration. Comparing the results with the existing ones in literature,it was shown that the proposed method can be applied to predict the critical pedestrian number for different footbridges,and it is simple and convenient; the established model is reasonable and correct; the closer the walking frequency of pedestrians approaches two times of the footbridge’s fundamental natural frequency,the less the pedestrians are needed to cause the footbridge’s large amplitude vibration; at that time,pedestrians’ a slight stimulation can cause large vibration of the footbridge; when the number of pedestrians exceeds the critical pedestrian number,the bridge ’s nonlinear vibration approaches a stable constant amplitude vibration; its linear vibration is a non-constant amplitude divergent one; pedestrian number per unit time,mass and damping per unit bridge length,and initial conditions have different level effects on the footbridge’s crowd-induced parametric vibration response amplitude.

关 键 词：人行桥 非线性 参数振动 临界人数 幅频曲线 

分 类 号：U441.3[建筑科学—桥梁与隧道工程] TU311.3[交通运输工程—道路与铁道工程]