Based on equivalent RMS structural deflection criteria

the simplified model is established for MR damper used in passive control. The model captures the salient features of MR dampers′ mechanical performance. For mitigating vibration caused by wind or earthquake

polynomial parametric representation of MR damper based on above model is need. The mechanical performance of MR dampers is related to the applied voltage

displacement amplitude and frequency.Using partial least squares in conjunction with the chebyshev polynomial respresentation

the expression for the simplified model is built

and is provided to determine the optimal MR damper. The modal damping of cable with MR dampers can be evaluated directly by using the existent universal estimation curve for estimating modal damping of cable with discrete viscous dampers. Then vibration mitigation of the cable using MR dampers is simulated.