Taking the bending stiffness, cable static sag and cable inclinded angle into consideration, the equations of space vibration of the cable-damper system are formulted 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 sovled 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 vibration modes with different cable parameters and damper parameters. The resutls show the dampingn 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.
In this paper, the governing equations of space nonlinear vibration for a stay-cable with viscous dampers are first derived. Bending stiffness, static sag and geometric non-linearity of cable are taken into account. The partial differential equations are discretized in space by the finite center difference approximation, then the nonlinear ordinary differential equations are obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy is proposed to analyze the nonlinear transient response of stay-cable with viscous dampers under arbitrary dynamic loading. The proposed method offers some advantages of accuracy and efficiency to deal with nonlinearity. Numerical examples including the short cable and the long cable under arbitrary loads are carried out to demonstrate the applicability of the proposed method and to verify the control efficiency of in-plane and out-of-plane coupling vibration
of stay-cable attached viscous dampers
Recent theoretical studies indicated that semi-active control using magnetorheological (MR) fluid dampers could provide better damping capability than viscous dampers for cable vibration mitigation. However, some challenging problems still remain in implementation of this smart damping technique to real engineering structures, e.g. how does the nonlinearity of MR dampers affect the system response? what are criteria of selecting MR damper size for an actual cable in design stage? which control strategies are cost effective and efficient for semi-active implementation? This paper tries to address these issues.
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