索梁结构面内耦合振动机理研究  

In-plane Coupled Vibration Mechanism of Cable-Beam Structure

作　　者：赵文忠 康健 梁栋 ZHAO Wenzhong;KANG Jian;LIANG Dong(School of Civil Engineering and Transportation,Hebei University of Technology,Tianjin 300401,P.R.China;Qugang Expressway Construction Department of Hebei Province,Dingzhou 073099,Hebei,P.R.China)

机构地区：[1]河北工业大学土木与交通学院,天津300401 [2]河北省高速公路曲港筹建处,河北定州073099

出　　处：《重庆交通大学学报（自然科学版）》2019年第8期20-26,58,共8页Journal of Chongqing Jiaotong University(Natural Science)

基　　金：国家自然科学基金项目(50808063)

摘　　要：为深入探究几何非线性条件下索-梁结构耦合振动问题,以3根斜拉索与简支梁组合体系为动力学简化模型,运用Hamilton原理建立考虑初始垂度的多索单梁体系非线性偏微分运动方程,利用Galerkin方法将其离散为忽略阻尼作用的二阶常微分方程组,并使用数值方法模拟了不同工况下拉索面内前两阶模态与主梁的耦合振动响应,着重分析了耦合作用的产生过程与影响机理。研究结果表明:当主梁振动固有频率、索面内一阶模态频率与二阶模态频率为1∶2∶1时,3根索一阶、二阶模态与主梁振动发生不同程度耦合,与单梁单索振动相比,3根索耦合时的振幅增大,拍频降低,表明索间存在相互作用;拉索的一阶模态振幅是控制结构瞬时安全的关键,而二阶模态振动对拉索长时间疲劳破坏有重要影响。In order to investigate the coupled vibration problem of the cable-beam structure under geometric nonlinear conditions,the three cables and simply supported beam combination system was used as a simplified dynamic model.The Hamiltonian principle was used to establish the nonlinear partial differential motion equation of multi-strip cable and single beam system with the initial sag.The Galerkin method was used to discretize the equation into second-order ordinary differential equations without damp effect.The in-plane coupled vibration responses of the first two modes of the cable and the main beam in different working conditions were simulated by numerical method,and the coupling process and impact mechanism were emphatically analyzed.The results show that when the natural frequency of the main beam vibration,the in-plane first-order mode frequency and the second-order mode frequency are 1∶2∶1,the first-order and the second-order mode of three cables are coupled with the vibration of the main beam to varying degrees.Compared with the single beam and single cable vibration,the amplitude of the three coupled cables increases,the beat frequency decreases,indicating the existence of interaction between cables;the first-order mode amplitude of the cable is the key to control the instantaneous safety of the structure,and the second-order mode vibration has an important influence on the long-term fatigue failure of cables.

关 键 词：桥梁工程 索梁结构 耦合振动 数值模拟 

分 类 号：U443[建筑科学—桥梁与隧道工程]