Coupled Vibration Analysis And Vibration Reduction Of Cable-beam In Cable-stayed Bridges

The cable of cable-stayed bridge has the characteristics of small damping.With the increase of span and length of cable,the vibration of cable is easily affected by the vibration of main girder.At present,the dynamic performance of main girder is neglected in the research of cable vibration reduction.For this reason,the dynamic characteristics of cable-girder coupling vibration and its effect on cable vibration damping performance are studied in this paper.At the same time,the optimization design and vibration reduction performance of cable damping with viscous damper,tuned mass damper and inertial damper installed on the main girder and between the cable and the main girder are investigated.The main contents are as follows:(1)The motion differential equations of cables without consideration of sag,cables with consideration of sag and cable-girder system with consideration of sag are derived.The principle of parametric vibration of cables with consideration of sag is analyzed by using the method of multiple scales,and the influence of parameters of cables on the vibration of cables without consideration of sag and cables with consideration of sag is discussed by using the fourth order Runge Kutta method.The resonance conditions of cable-beam coupling system and the influence of amplitude and frequency of external excitation on the vibration of cable-beam coupling system are further studied.(2)Tuned mass damper(TMD)and Tuned mass inertia damper(TMDI)are respectively considered to be installed inside the main girder.The mathematical model of cable-girder-damper is established,and the equations of motion of cable-beamdamper system are derived.The damping performance of TMD and TMDI on cable-girder coupling system is studied;The influence of damper parameters on damping performance of damper is analyzed.Through comparison,it is found that TMD can better control cable amplitude than TMDI,while TMDI can improve the control effect of damper and main girder relative displacement.The sensitivity and robustness of the damper parameters are discussed.(3)The vibration damping performance of the system with Viscous damper(VD),Tune the inertial damper(TID)and Tune viscous mass damper(TVMD)installed between the main girder and the cable is compared and studied.The cable-damperbeam models are established respectively,and the complex characteristic equations of the system are derived.The influences of damper stiffness,inertial coefficient and installation position on the modal damping ratio of the system,as well as the influence of the frequency ratio between the main girder and the cable on the damping performance of the damper are explored.By comparing the damping performance of VD dampers,it is found that TID and TVMD can achieve better damping effect.