Theoretical And Numerical Analysis On The Parametric Vibration Of Cables In Cable-stayed Bridges

The long span cable-stayed bridges are widly used for large-span bridges. As the main members to support the weight of the bridge, the stayed cables are prone to voilence vihibit parametric oscillation with large amplitude under the wind or traffic loads due to it's high flexibility ,low damping and small mass.This oscillation can greatly affect the performance of the bridge. In order to improve the design of cable-stayed bridge it is important to study the mechanism of the vibration and perform numerical analysis.First of all, the dynamic characteristics of the cables with different sags are investigated and the reason which cause the varition are discussed in this dissertation. And then, taking the idealized excitation and nonidealized excitation into consideration, the models of parametric oscillation for cables are built up. The nonlinear oscillation differential equation is got by Galerkin method. According to the equation, the influence of parametric excitation, external excitation, nonlinear terms and damping are investigated by multiple-scale method. Response curve is obtained for main resonance and parametric resonance by numerical analysis with Runge-Kutta method . In order to obtain the coupling nonlinear vibration equations, a coupling vibration model of in-plant and out-of-plant oscillation is built up. Multiple-scals method is used for calculating the equation set. The response curve of cables which in three-dimensional space is detemined for in-plant and out-of-plant coupling vibration by numerical method. Based on ANSYS, according to the characteristic of parametric oscillation, three-dimensional models for cables which take stress intensification and geometric nonlinearity into consideration are built up for transient analysis .The results show that there is a little distinction between finite element analysis and numerical analysis. At last, a three-demensinal finite element model is built up for a real bridge. According to the principle of parametric oscillation, we can find out which cable may occur main resonance or parametric resonance.The results can provide references for designing of cable-stayed bridges.