In this paper we have studied the effect of end stops in an isolator. While subjected to excessive base excitation the stops prevent the system from excessive relative displacement particularly around the resonance frequency. Although stoppers prevent the undesired motion they increase the transmitted force that is undesirable in suspension systems. This system is modeled as a piecewise linear system where the nonlinearity cannot be considered small. Therefore we have adopted an averaging method which leads to analytical frequency response of the piecewise linear system at resonance. Using this analytical method we are able to obtain the range of the parameters, which minimize the relative displacement of the system. Further more using the RMS optimization methods the transmitted force in the system is optimized.

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