Numerical simulation of vibration control for stay cable using MR dampers

In order to overcome long span cables vibration, a calculation model for the cable-damper system was formulated by Galerkin method based on the Hamilton principle. The motion of the cable was computed by using a finite series approximation with a Galerkin method. Runge-Kutta method was applied for the numerical solution of initial value problems with oscillating solutions. A static deflection shape was taken as an addition shape function to improve the sine series convergence. According to experimental set-up, the 154 m long cable in the 3rd Qianjiang Cable Stayed Bridge was numerically calculated. A nonlinear hysteretic bi-viscous model was identified for MR dampers. The displacement signal at observation point was driven by harmonic planar loads, and transformed by Hilbert. The equivalent cable modal damping ratios attributed to MR dampers were predicted, and the relationship among the equivalent modal damping ratios, the system frequency, the voltage imposed and displacement responses at the point of cable was pursued. The phenomena and conclusions from simulation guiding the experimental operation could be certified by full scale experimental study. It is shown that MR dampers to the cable can more significantly reduce cable vibration than oil dampers do; the resonant frequencies of the cable with MR dampers have a little increased change; there is optimum voltage on which the maximum modal damping ratio can be achieved.