From experimental results, the magneto-rheological (MR) damping varying with relative velocity is modeled through a piecewise-linear model. Periodic motions in a semi-active suspension system with such a piecewise-linear MR damping are investigated. The theory of discontinuous dynamical systems is employed to determine the grazing motions in such a system, and the mapping technique is used to develop the mapping structures of periodic motions. The periodic motions and stability are predicted analytically and verified numerically. The stability and bifurcation analyses of such periodic motions are performed, and the parameters for all possible motions are developed. This model is applicable for the semi-active suspension system with the magneto-rheological damper in automobiles. Further investigation of magneto-rheological damping with full nonlinearity should be completed.
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