Impact of a body against a rigid wall. Problem involving non-smooth and history dependent energy dissipation mechanism

TL;DR

This paper analyzes the impact of a viscoelastic body against a rigid wall, incorporating non-smooth energy dissipation and history-dependent effects, using analytical and numerical methods.

Contribution

It introduces an analytical approach to model impact involving fractional viscoelasticity and Coulomb friction, with solutions compared to numerical results.

Findings

Analytical solutions in convolution form for impact problem

Comparison between analytical and numerical solutions

Insights into energy dissipation mechanisms during impact

Abstract

We study the impact of a body against a rigid wall. The body consists of a rigid block and a viscoelastic rod described by the fractional Zener model. Translatory motion of a body is influenced by the dry friction, described by the set-valued Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form. These solutions are compared with the ones obtained by using the numerical method.