Maximum modal damping of cable space vibration control with viscous damper in cable-stayed bridge

Taking the bending stiffness, cable static sag and cable inclined angle into consideration, the equations of space vibration of the cable-damper system are formulated in this paper. Applying the variable separation strategy and center difference method, the partial differential equations are discrete in space and a set of complex eigenvalue equations are solved by state space method. Then both the maximum modal damping ratio and the optimal damper parameters are obtained. Some typical stay cables are investigated for both the in-plane and out-plane vibration modes with different cable parameters and damper parameters. The results show the damping ratio for the first in-plane mode is significantly affected by the cable static sag only, but those for the other modes are affected slightly, and cable static sag do not affect the optimal damper parameter for all modes. However the bending stiffness will changes both the maximum modal damping ratios and the optimal damper parameters. Some valuable suggestions are proposed for the optimal damper design.