Eur. Phys. J. B (2012) 85: 101
https://doi.org/10.1140/epjb/e2012-20616-3

Regular Article

Dry friction: motions – map, characterization and control

¹ Laboratoire de Mécanique, Département de Physique, Faculté des Sciences, Université de Yaoundé, B.P. 812 Yaoundé, Cameroon
² Nonlinear Physics and Complex Systems Group, Département de Physique, École Normale Supérieure, Université de Yaoundé I, P.O. Box 47 Yaoundé, Cameroon

^a e-mail: fozap2002@yahoo.fr

Received: 26 July 2011
Received in final form: 8 December 2011
Published online: 26 March 2012

Abstract

We consider a simple model of spring-mass block placed over a constant velocity v rolling plate. The map of the dynamic is presented in the (v,r) space where r accounts for the possible variation of the periodic shape profile of the rolling carpet. In order to characterize each type of motion, we found that evaluating the area of the phase space trajectories is more relevant than attempting on one hand, to solve analytically the asymptotic behavior, or on the other hand, to obtain an equivalent of the entropy and the free energy. First-order transition reveals to be the characteristic route from one type of motion to another. Later, we investigate the influence of the classical TMD¹ and TLCD² on the dynamic of this mass. Moreover, we numerically study the effects of a modified TMD. Reduced order parameter provides a quick overview of the whole system than phase space representations and bifurcation diagrams. Comparison of performances in the (v,r) space is made. It reveals the efficiency of the modified TMD. It comes out that the new TMD we designed stabilizes the system better than the two above control systems.