Analysis of Vibro-Impact System with Ideal Excitation and Various Friction Models

Abstract

In this paper, the dynamic analysis of a vibro-impact system with ideal excitation and various friction models is performed. A physical model of an oscillating mechanical system with possible impact occurrence is presented and the corresponding mathematical model is derived by using Lagrange’s equations of motion. To describe interaction between impact element and environment, three different friction models are considered: Coulomb, viscous and Coulomb-Stribeck model. Newton’s impact law with a coefficient of restitution is employed to describe relationship between pre-impact and post-impact velocities. The dynamic behavior of the vibro-impact system under the ideal excitation, where the system does not influence the excitation source, is investigated for each friction model by numerically solving the governing equations. The results of numerical analysis are presented through amplitude-frequency diagrams, displacement-time responses and phase portraits. The main objective is to determine the influence of different friction models on amplitude-frequency diagrams, particularly on the regions exhibiting impact and non-impact behavior. For parameter regions with multiple coexisting solutions, basins of attraction are constructed to illustrate the dependence of the system regime on initial conditions.