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We explored vibrations of a single-degree of freedom oscillator with a magnetorheological damper subjected to kinematic excitations. Using fast and slow scales decoupling procedure we derived an effective damping coefficient in the limit of high frequency excitation. Damping characteristics, as functions of velocity, change considerably especially by terminating the singular non-smoothness points. This effect was more transparent for a larger control parameter which was defined as the product of the excitation amplitude and its frequency.

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Vibrations of a single‐degree‐of‐freedom oscillator with a hysteretic damper subjected to kinematic excitations in a high frequency limit have been explored. By using of two time scales expansion we derived an effective damping coefficient. It has been shown that in the limit of the high excitation frequency the hysteretic loop could be eliminated for the slow time scale dynamics. For simplicity, to examine the effect of hysteresis we used the model of a single hysteron. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)