Eur. Phys. J. B 70, 353-361 (2009)
https://doi.org/10.1140/epjb/e2009-00226-0

Nonlinear spring model for frictional stick-slip motion

Département de Physique, Laboratoire de Mécanique, Faculté des Sciences, Université de Yaoundé I, B.P., 812 Yaoundé, Cameroun

Corresponding author: ^a kdjuidje@yahoo.fr

Received: 8 February 2009
Revised: 12 May 2009
Published online: 3 July 2009

Abstract

Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k₀. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k₀. The system also displays resonance at fractional frequencies of the oscillator.