Properties of impact events in the model of forced impacting oscillator: Experimental and numerical investigations

The paper deals with the studies of the forced impacting oscillator when taking into account the dry and viscous resistance as well as the generalized Hertz contact law during an impact. Numerical investigations of the mathematical model are accompanied by validations obtained with an experimental rig. To study the solutions of the mathematical model, the sequences of impacts, when the system evolves in periodic and chaotic modes, is used. The statistical properties of chaotic impact events are considered in detail. In particular, successive iterations of the impact map, autocorrelation function and coefficient of variation for the impact train, histograms for the inter-impact intervals and values of obstacle penetrations are analyzed. It is revealed that the impact sequence is stationary but non-Poissonian and contains temporal scales that do not relate to the external stimulus. This sequence can be described by a bimodal distribution. The findings are confirmed by the analysis of experimental data.