Stability And Dynamic Performance Analysis Of Parametric Vibration Of Stay Cable In Cable-Stayed Bridge With Super-Long Span

With the construction of the long-span cable-stayed bridge,the real engineering application of super-long stay cable with low damping and large flexibility reduces the cable's vibration frequency,and widens the range of vibration modal frequencies,which easily causes large-amplitude parametric vibration of cables,and poses a great threat to the safety and service life of cables.Therefore,it is great significant to accurately analyze the parametric vibration characteristics and mechanism of the cable in the long-span cable-stayed bridge.In this paper,the longest cable in Hutong Yangtze River Bridge,with a main span of 1092 m,is taken as the representative cable.Taking the cable's vibration induced by the bridge deck displacement excitation as the research object,the combination of theoretical analysis and numerical calculation is applied to analyze the cable's nonlinear parametric vibration characteristics and its stability,which provides a basic theory for the vibration control of the super-long stay cable.The research contents of this thesis include the following aspects:(1)Considering the effects of cable's sag and chord component of cable's self-weight,the static equilibrium configuration of the stay cable was analyzed.The stay cable's sag curve equation,with high precision and convenient for its dynamic analysis,was established.Furthermore,taking cables in real engineering as an example,the sag equation was verified to be correct,and its applicability was discussed.(2)Considering the in-plane vibration of the stay cable with the axial displacement excitation at the end,the modal motion equation of parametric vibration was established based on the setup of the sag equation.The multi-scale method and Lyapunov stability theory were used to investigate the motion stability of the cable when the 1:2,1:1 and 2:1 resonance occur.The fourth-order Runge-Kutta method was adopted to study the influences of damping,external excitation amplitude and excitation frequency on the stay cable's vibration characteristics,which provides the basis for the cable's subsequent coupled vibration analysis.(3)Considering in-plane and out-of-plane coupled vibrations of the stay cable with end displacement excitation,conditions and bifurcation behaviors for 1:1 and 2:1 resonance were discussed by means of averaging method.By means of numerical integration method,some impacts of damping,external excitation amplitude and excitation frequency on the cable's vibration properties were analyzed,and the cable's chaotic motions were preliminarily judged.(4)Considering the coupled effect of stay cable and bridge deck,conditions for the main resonance and internal resonance of the system were theoretically judged.The response characteristics of the system under free vibration and forced vibration were discussed,respectively.The effects of initial disturbance,system damping,mass ratio,external excitation amplitude and excitation frequency on the nonlinear vibration response of the stay cable were analyzed.