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

## TL;DR

This study investigates the dynamics of a forced impacting oscillator through experimental and numerical methods, revealing complex impact sequences that are stationary, non-Poissonian, and characterized by bimodal distributions.

## Contribution

It combines experimental validation with numerical modeling to analyze impact sequences, including chaotic behavior and statistical properties, in a forced impacting oscillator.

## Key findings

- Impact sequences are stationary but non-Poissonian.
- Impact sequences exhibit bimodal distribution characteristics.
- Experimental data confirms numerical analysis results.

## Abstract

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