A Research On Nonlinear Vibration Of Stayed Cable Subjected To Deck Excitation

In the past20years, the span of cable-stayed bridge has significantly increasedand many large cable-stayed bridges have been built. With the increasing of thecable-stayed bridge span, the stayed cable also gets longer and longer. As one of themain bearing components of cable-stayed bridge, the stayed cable has some goodcharacteristics, such as light weight, large flexible and low damping. Due to theexternal load effect, the deck and bridge tower are likely to vibrate. As both ends ofthe cable connected to the bridge tower and the deck, the cable may occurs nonlinearvibration because of the deck excitation. Therefore, the study of cable nonlinearvibration has an important theoretical significance and engineering valuable.Based on the research of scholars both inland and abroad, in this paper, thevibration of stayed cable which induced by the deck excitation was taken as the mainresearch object; a precise deck-cable-tower model was established; a series of studyhas been done on the nonlinear vibration of stayed cable.With the deck-cable-tower model, the in-plane nonlinear oscillation differentialequations were deduced. And also multi-scale method is used to analyze theresonance range of cable in-plane vibration. In the numerical analysis, the Garlerkinmethod was used to discrete the nonlinear oscillation equations.In ideal condition,the influence of the system frequency ratio, the deck excitation amplitude, the initialdisturbance of tower, the initial cable tension and the dip angle of cable on the cablevibration was analysed by Runge-Kutta numerical analysis method.According to the cable’s out-of-plane vibration phenomenon, the out-of-planenonlinear oscillation differential equations have been deduced and Multi-scalemethod has been used to analyze the possibility of cable out-of-plane vibration.Keeping the same deck excitation, the influence on cable out-of-plane vibration fromthe tower, the cable itself and the deck has been analysed.Considering the in-plane and out-of-plane vibration may occur at the same time，the characteristics of both in-plane and out-of-plane cable vibration have beenanalysed. The cable nonlinear oscillation differential equations when consideringboth the in-plane and out-of-plane vibration was deduced. Multi-scale method is usedto analyze the possibility of in-plane and out-of-plane cable vibration. The couplingrelation of in-plane and out-of-plane vibration is analyzed by numerical method whenconsidering the deck excitation frequency and amplitude, the initial disturbance ofthe cable, the initial cable tension and so on.On a project background, a cable-stayed-bridge finite element model is built up by using ANASYS. According to the modal analysis, the dynamic characteristics ofthe bridge model can be obtained. At the same time, the fundamental frequency ofevery cable was calculated by using theoretical method. Then the cables which mayvibrate by comparing the fundamental frequency of cable with the first30frequencies of the cable-stayed-bridge were found out.