Research On Parametric Vibration Active And Semi-active Control For Super Long Stay Cables

Cables in cable-stayed bridges are prone to exhibit parametric vibration of large amplitude due to their small rigidity,small mass and low damping.With the increace of the span lenth of cable-steyed bridges,stay cables become longer and longer.Hence,large-value parameter resonances are extremely easy to occur.Therefore,it has become a hot issue for researchers related fields vibration control to research the vibration control methods for the large-value parameter resonance responses of stay cables.Parametric vibration control of stay cables can be roughly classified as passive control,active control,semi-active control and intelligent control.Semi-control is divided into different types due to different kinds of dampers,and the semi-active control using magnetorheological(MR)damper is called magnetorheological damper semi-active control(MR semi-active control for short).By combination of analytic solutions and numerical computations,this paper focuses on the the active and MR semi-active control of nonlinear parameter vibration of extra long cables in cable-stayed bridges.The active and MR semi-active control systems for in-plane parametric vibration under axial ideal displacement excitation and parametric vibration considering the coupling interaction between the stay cable and bridge deck are designed respectively.Not only the characterstics of the vibration and controlling force but also the influence of system paramaters of these control systems are analyzed in this paper.The main contents in each chapter are shown below.(1)Contraposing to the in-plane parametric vibration of stay cables under axial ideal harmonic excitation,the differential equation of cable parametric vibration considering the influence of gravity component was established.The active control system was designed based on linear quadratic regulator(LQR)classical optimal control theory and the analytical expressions of stiffness coefficient and damping coefficient of system were derived.The influence of each parameter on the active control effect and the charactiristics of active controlling force were numerically analyzed.The stability and occurrence conditions of the primary resonance and the primary parametric resonance of the controlled stay cables were theoretically studied by using the multi-scale method.The influence of stiffness coefficient and damping coefficient on the stability and occurrence conditions of the parametric vibration of stay cables was analyzed.(2)Contraposing to the parametric vibration of stay cables considering the coupling interaction between the stay cable and bridge deck,the differential equation of cable parametric vibration considering the influence of gravity component was established,thus the model had two degree of freedoms.The LQR method was used to design the active controller,and both free vibration and forced vibration characteristics of the cable parametric vibration active control system were numerically analyzed respectively.The influence laws of weight ratio,bridge deck-cable frequency ratio,bridge-cable mass ratio and external excitation on the dynamic characteristics of the control system were discussed.The occurrence conditions and stability of parametric vibration of the system were analyzed by using the multi-scale method.(3)Contraposing to both the in-plane parametric vibration of stay cables under axial ideal harmonic excitation and the parametric vibration of stay cables considering the coupling interaction between the stay cable and bridge deck,the magnetorheological damper semi-active control systems was designed on the basis of active control systems.The effect of semi-active control effect and controlling force characteristics under different parameters of MR damper were compared and analyzed.Finally,the compared of semi-active control and active control verified that the effect of semi-active control is close to which of active control,and it was of high efficiency.