Random vibration with inelastic impact: equivalent nonlinearization technique

The Hertzian contact model, due to its inherent elastic-property, is confined to analyze the dynamic response of vibrating system with elastic impact. A modified Hertzian contact model which is developed through recent experiments, however, can include the properties of inelastic impact and provides an opportunity to break the aforementioned limitation. In this manuscript, the random response of vibrating system with inelastic impact which is described through the modified model is investigated by the equivalent nonlinearization technique. One class of nonlinear stochastic systems with undetermined parameters is elaborately selected, and the stationary probability density of any element is attainable. The equivalent nonlinear system of the original system is selected in the given class and the undetermined parameters are determined through minimizing the mean-square difference. The joint probability density of system displacement and velocity, and then the statistics of system response are analytically obtained through the equivalent nonlinear system. With Monte-Carlo simulations as the standard, numerical results verify the effectiveness of the proposed procedure and the higher precision compared to stochastic averaging technique.