Free And Vortex-Induced Vibrations Of A Cable-Stayed Bridge With A Single Tower

The cable-stayed bridge has become very popular over the last decades,because it has a strong economic competiveness in bridge engineering with its aesthetic appeal,structural efficiency and enhanced stiffness.At the same time,with the introduction of the high-strength materials,combined with rapid development of the technology,cable-stayed bridge has stepped into the ranks of large span bridges,and becomes slender.However,the dynamical characteristic of the cable-stayed bridge excited by seismic,wind/rain and traffic loads are becoming more and more prominent.Consequently,an accurate analysis of the natural frequencies and mode shapes of the cable-stayed bridge is fundamental to the solution of its dynamic response about these nonlinear behaviors.As a kind of vibration phenomenon with limited amplitude which is subjected to very low wind speeds of the large-span bridge,vortex-induced vibration has been studied with particular attention to avoid fatigue damages and the reduction of travel safety/or comforts levels for the users.Though it would not cause the catastrophic damage as the flutter of the structure functions,but excessive and unanticipated phenomenon about the bridge destruction due to vortex-induced vibration has occurred frequently.Accordingly,it is very important to study the vortex-induced vibration of the cable-stayed bridge,and in further,to avoid the occurrence of these phenomenon or to limit its amplitude within a certain safety range,which is of great significance to bridge engineering.In this paper,an overview of the investigation on the wind-induced vibration of the bridge is briefly provided,and especially,it has explored the mechanism of vortex-induced vibration,as well as its research methods.Free vibration analysis of the cable-stayed bridge that consists of a simply-supported two-cable-stayed deck beam and a single tower is presented.The bridge deck and tower are modeled by using Euler-Bernoulli beam method.The partial differential equations that govern vibrations of the stay cables,tower,and segments of the deck beam,respectively,are established by using a continuum system,as well as their boundary and matching conditions.And then,once the natural frequency is obtained by solving the equation,which can be used to solve the mode shapes of the cable-stayed bridge.Finally,numerical results can be used to explore the effects of the stiffness of tower on the characteristics of the bridge,and it also study the possible dynamical behavior of the cable-stayed bridge when its symmetry breaks due to small variations of the geometry parameters,such as length and initial sags of the cables.Besides,vortex-induced vibration of a cable-stayed bridge with a single tower are presented in third chapter.Here,a continuum system is used to establish the model of cable-stayed bridge,the distributed vortex-shedding force on the deck beam is introduced to obtain the vortex-induced vibration equations of the cable-stayed bridge on the basis of Ehan-Scanlan model.The coupled governing partial differential equations is discretized into a set of ordinary differential equations by using Galerkin method,and then the dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB.Numerical results can be used to explore the effects of initial dynamic configuration and geometric nonlinear terms on the response of vortex-induced vibration of the cable-stayed bridge,and it has also compared the vortex-induced vibration response between two cases by modeling the tower as rigid or flexible body.Finally,the switched system is adopted to describe the coupled dynamical behaviors of the cable-stayed bridge between mode jumping and vortex shedding force when allowing for the effective length of the cables may switch between two different values.Here,the bifurcation behavior of the vortex-induced vibration is analyzed by regarding the tower stiffness and pneumatic coefficient as the bifurcation parameters,combined with the time history response and phase diagram.The study can provide a theoretical basis for the initial design and vibration control of the cable-stayed bridge.