Stochastic Responses for the Vibro-Impact System under the Broadband Noise

The stochastic averaging is applied to derive the random responses of the SDOF vibro-impact system with one-side wall under additive and multiplicative broadband noise, where the impact is described by the modified Hertzian contact model. Compared with the popular simplified classical model (i.e., x+), the whole impact process is captured by the modified Hertzian contact model without any assumptions. One example is given to illustrate the proposed technique. The comparison between the analytical results and those from Monte Carlo simulations manifests the accuracy of the proposed technique. It should be pointed out that the technique proposed in this paper is powerful for the cases of weak excitation and big enough bandwidth of the broadband noise. Finally, the influences of various parameters are also discussed in detail.