Vibration Control And Simulation Analysis Of Cables For Cable-stayed Bridges

Stay cable is the main support system and an important component of cable-stayed bridges. Stay cables of the long-span bridges are susceptible to vibration under wind loading, or wind incorporated rain excitation, or traffic loading. Large-amplitude vibration of cables may reduce the life of cables and threaten safe traffic and restrict the development of large span cable-stayed bridges. The vibration and its control of the stay cable is extensively studied, and the control effect of the active, passive control and semi-active control by using MR damper is analyzed.The development of cable-stayed bridges and serious damage caused by the large vibration of cable are introduced in this paper. The cable vibration types, research status and control measures(including aerodynamic measures, structural measures and damper measures) are reviewed. Damper measures are emphatically analyzed, and the several kinds of dampers used commonly has been carried on the comprehensive comparison.Taking the bending stiffness, cable sag and cable inclination into consideration, the linear partial differential equation of free vibration of the cable-viscoelastic damper system was deduced. The generalized characteristic root equation has been obtained combining with the method of separation of variables and center difference method. Deriving the stiffness, mass and damping matrix of the vibration equation, and the complex characteristics root value was solved through the state space method. Both the maximum modal damping ration and the optimal damper coefficient are obtained, then the practical suggestions are proposed for the design of the dampers.Considering the cable sag, bending stiffness and geometric nonlinearity, the space nonlinear vibration equations of the cable-viscoelastic damper system is deduced and obtaining the corresponding mass matrix, stiffness matrix, damping matrix and nonlinear force matrix. Then the Newmark-β method is used to solved the vibration equations of the cable-damper system, and the nonlinear transient response examples is analysised. Combined with the optimal LQR theory, the displacement respond of the cable at the condition of uncontrolled, active, passive was analyzed respectively, and the SIMULINK models corresponding to the MATLAB are established. And the damper’s control effect of cable under various loading conditions is intuitively and clearly verified through the displacementtime curves.Based on the directions of both the velocity and the displacement, the semi-active control algorithm was presented. The vibration response in-plane is analyzed by using the difference discretization model of the cable-MR damper system and the semi-active algorithm. MR dampers are explored in detail by using the Spencer phenomenological model. The evaluation index of vibration effect is the displacement of vibration along the whole length of the cable and for the whole period of time. The displacement respond of the cable at the condition of semi-active by using MR damper is analyzed, and the SIMULINK models corresponding to the MATLAB are established.