A novel dry friction modeling and its impact on differential equations computation and lyapunov exponents estimation

Abstract

A novel dry friction modeling and its impact on differential equations computation and Lyapunov exponents estimation are studied in this paper. A brief review of some existing standard friction laws are presented and novel continuous friction model is proposed, which takes into account some elements of the mentioned friction models. We show that our continuous friction model is suitable for analysis of stick-slip vibrations caused by dry friction and is more efficient from a computational point of view in comparison with the other presented friction models. Its advantages are illustrated and discussed using a two degree-of-freedom model. Although there are numerous works in the scientific literature dedicated to stick-slip vibrations, we consider a rigid body lying on a belt which moves at non-constant velocity that is less investigated. The behavior of the system is monitored via standard motion analysis. Time series, phase portraits, bifurcation diagram as well as the Lyapunov exponents are reporte