Numerical Analysis Of In-plane Parametric Vibration And The Controlling Measures For Stay Cables

As a result of low damping and great flexibility characteristics, cables incable-stayed bridge are easily induced large amplitude vibration under axialdisplacement excitation. Generally speaking, when the natural frequencies of globalmodal in a cable-stayed bridge are a certain times that of the cables, large amplitudevibration can be easily induced by micro excitation which causes serious threat to thesafety and service performance of the bridges. Therefore，it is necessary to study thecharacteristics of vibration in cables and take effective controlling measures for themaintenance of cables.This paper mainly focuses on the parametric vibration causedby the movement of decks. The development of cable-stayed bridges and the currentproblem of cable vibration in the practical application are introduced. Based on theYangpu Bridge, the mechanism of parametric vibration, forms of damage, influencingparameters and controlling measures are studied. The research contents and researchresults are as follows:(1) The equation of cable-bridge uncoupled parametric vibration under axialdisplacement excitation is deduced. In the model, the first modal of the cable is takeninto accounted. The characteristics of vibration in cables are analyzed by means ofRunge-kutta numerical analysis. The influence of those parameters, such as excitationfrequency, excitation amplitude, damping, inclination angle, initial cable forces andso on, are studied.(2) The first ten modal with the natural frequencies of cables and the first twentymodal frequencies of the whole stayed-bridge are obtained by the modalanalysis.Comparing the frequencies above，the cables that may exhibit vibrationcould be obtained.(3) Based on the effect of the sag and the coupling interaction between the staycable and the deck, cable-bridge analytical models of vibration are presented. In thefirst model, the first two modals of the cable are considered, and thethree-degree-of-freedom coupled non-linear differential equations are gained. In theother one, the first modal of the cable are considered, and the two-degree-of-freedomcoupled non-linear differential equations are gained. The influence of thoseparameters, such as the initial displacement of cable and deck, the stiffness of girder,damping are studied. (4) The cable-damper system analytical models are presented. Based on LQcontrol method, the active control law is obtained to suppress parametric vibration ofstay cable. Matlab program are written as passive control law to suppress parametricvibration of stay cable.