考虑弯曲刚度的索桥耦合系统振动特征分析  

Analysis of the Vibration Characteristics of the Cable Bridge Coupling System with Bending Stiffness Considered

作　　者：闵光云 刘小会[1,2] 刘菊芳 孙测世[1,2] 蔡萌琦 MIN Guangyun;LIU Xiaohui;LIU Jufang;SUN Ceshi;CAI Mengqi(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China;State Key Laboratory of Bridge and Tunnel Engineering in Mountainous Areas,Chongqing Jiaotong University,Chongqing 400074,China;School of Architecture and Civil Engineering,Chengdu University,Chengdu 610106,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074 [2]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆400074 [3]成都大学建筑与土木工程学院,成都610106

出　　处：《西南大学学报（自然科学版）》2021年第12期180-190,共11页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(51308570,51808085,51507106);重庆市研究生科研创新项目(CYS19240);重庆市创新训练项目(S201910618016);重庆市科委基础科学与前沿技术研究项目(cstc2017jcyjAX0246);成都市国际科技合作资助项目(2020-GH02-00059-HZ).

摘　　要：本文建立了拉索—桥面耦合的非线性振动模型,求解了该耦合共振模型的位移响应,还考虑了弯曲刚度对拉索位移响应的影响.首先通过哈密顿变分准则求得了拉索的振动方程,接着以动张力为媒介求得了拉索—桥面耦合模型的振动方程,基于Galerkin法将该振动方程转化为常微分方程,利用多尺度法分析了该常微分方程的共振模式,并介绍了四阶龙格-库塔(Runge-Kutta)方法的计算原理,最后通过数值算例对该微分方程进行了系统地分析.算例分析表明:拉索面内、面外、桥面之间的耦合显著,拉索面内的振动位移远大于面外的摆动位移;针对小直径拉索动力学分析时,可忽略弯曲刚度对拉索振动特征的影响,但针对特大直径拉索动力学分析时,需考虑弯曲刚度对拉索振动特征的影响;对于小跨径、小张力拉索,弯曲刚度不会改变拉索共振的性质,但会使得拉索发生共振的条件具有向左偏移的趋势,且面内偏移的趋势不明显,但面外偏移的趋势很显著;对于大跨径、大张力的拉索,可忽略弯曲刚度对拉索发生共振条件的影响.In this paper,a nonlinear vibration model of cable and bridge coupling is established,the displacement response of the model is solved,and the influences of bending stiffness on the displacement response of the cable are considered.Firstly,the vibration equation of the stay-cable is obtained by the Hamiltonian variational principle.Then,the vibration equation of the cable and bridge coupling model is obtained with dynamic tension as the medium.Based on the Galerkin method,the vibration equation is transformed into an ordinary differential equation,the common vibration mode of this ordinary differential equation is analyzed with the multiple scales method,and the four-order Runge-Kutta method is described.Finally,the vibration equation is systematically analyzed with a numerical example.The results show that the coupling between in-plane and out-of-plane of cable and bridge is significant,and in-plane vibration displacement of cable is far greater than out-of-plane swing displacement of cable;that for the dynamic analysis of small-diameter cables,the influences of bending stiffness on vibration characteristics of cable are negligible,but for the dynamic analysis of large-diameter cables,the influences of bending stiffness on vibration characteristics of cable should be considered;that for small-span and small-tension cables,the bending stiffness does not change the nature of their resonance,but the conditions of resonance tend to have a left deviation,and the trend of in-plane displacement is not obvious,but the trend of out-of-plane displacement is significant;and that for the long-span and large-tension cables,the influences of bending stiffness on the condition of resonance of cable can be ignored.

关 键 词：拉索 耦合 共振 多尺度法 位移响应 

分 类 号：O322[理学—一般力学与力学基础] U441.3[理学—力学]