Analysis of Impact Chattering

TL;DR

This paper investigates impact chattering in mechanical models, establishing criteria for initial conditions that lead to chattering, and explores control methods to suppress it, with applications demonstrated through examples.

Contribution

It introduces a novel criterion for identifying initial data sets that cause impact chattering and applies Pyragas control to suppress the phenomenon.

Findings

Criteria for initial data causing chattering are established.

Chattering can be generated and controlled using Pyragas control.

Impact chattering is demonstrated in the Moon-Holmes model.

Abstract

In this paper, mechanical models with Newton's Law of impacts are studied. One of the most interesting properties in some of these models is chattering. This phenomenon is understood as the appearance of an infinite number of impacts occurring in a finite time. Conclusion on the presence of chattering is made exclusively by examination of the right hand side of impact models for the first time. Criteria for the sets of initial data which always lead to chattering are established. The Moon-Holmes model is subject to regular impact perturbations for the chattering generation. Using the chattering solutions, continuous chattering is generated. To depress the chattering, Pyragas control is applied. Illustrative examples are provided to demonstrate the impact chattering.