Study On Vibration Control Of Stay Cable System With Tuned Inertial Damper Based On Complex Modal Analysis

The vibration control of stay cables is the key to ensure the long-term safe operation of cable-stayed bridges.Tuned inertial damper(TID)has become an effective measure for vibration control because it can provide large damping near the tuning frequency,and also provide certain damping effect when it is higher than the tuning frequency.In this paper,the complex modal analysis method is used to explore the vibration reduction of single stay cable and double cable net system with viscous damper(VD)and tuned inertial damper.Based on the tension string theory,the characteristic equation of the damper cable system is established and solved,and the parameter optimization is realized.The main contents are as follows:(1)The influence of damper position on the vibration reduction of “VD-single-cable”and “VD-double-cable” systems is compared and analyzed,and the necessity of using damper to connect the middle part of cables to reduce the vibration of cable net is clarified.By establishing the characteristic equation of the cable system,the complex modal analysis and fixed point iteration method are used to realize the numerical solution.The modal damping characteristics of the cable system with different damping coefficient and damper position under different double cable length ratio and natural frequency ratio are given.(2)The characteristic equation of “TID-single-cable” system is established,and the“bifurcation point” method is used to optimize the first modal damping ratio.The optimal stiffness coefficient and the optimal damping coefficient are obtained.The variation law of the optimal modal damping ratio at the “bifurcation poin” under different mass coefficients and damper positions is analyzed,and the mechanism of using TID to achieve the optimal damping ratio of the first-order modal is studied.(3)The characteristic equation of “TID-double-cable” system is established.Two kinds of double cable length ratio and natural frequency ratio are selected.The "bifurcation point" method is used to optimize the first and second modal damping ratio respectively,and the optimal stiffness and damping coefficient are obtained.The variation law of the optimal modal damping ratio at the “bifurcation point” under different mass coefficients and damper positions is analyzed.The effect of increasing the installation position of TID on the optimal damping ratio of double-cable-damping system is revealed.