In this work we have studied the effect of stoppers in quarter car model. While in rough roads these stoppers prevent the system from excessive displacement around the resonance frequency. Although stoppers prevent the undesired motion they increase the transmitted force that is undesirable in suspension systems. In order to optimize between the relative displacement and transmitted force an analytical model is considered. The piecewise linear system is the model of presented nonlinearity which cannot be considered small. Therefore standard perturbation methods are not able to provide an analytical solution. For this case we have adopted an averaging method which leads to frequency response of the piecewise linear system at resonance. In order to confirm the results obtained by averaging method an experimental device is fabricated and frequency response of the system is measured. The experimental frequency response is in very good agreement with analytical approach and numerical simulations. Sensitivity analysis methods are used to minimize the cost function of maximum relative displacement in frequency domain. The range of the parameters that minimizes the cost function where certain amount of clearance exists in the system are obtained.

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