11.1.1 Introduction

In the literature, many studies about the behaviour of nonlinear models can be found within the last twenty years. Brogliato [Brogliato (1996)] and Palmov [Palmov (1998)] give in their respective books numerous nonlinear mechanical models. Among these models, we are interested in those involving friction laws.

Authors especially study mechanical models with a finite number of degrees of freedom involving frictions terms and submitted to dynamical solicitations. Some of these papers provide mathematical results of existence and uniqueness [Jean and Pratt (1985); Laghdir and Monteiro Marques (1995); Monteiro Marques (1994); Matrosov and Finogenko (1995); Matrosov and Finogenko (1996b); Matrosov and Finogenko (1996a); Trinkle et. al. (1997)]. Some others investigate physical behaviours without dealing with theoretical results: some works present friction laws issued from experiments [Anderson and Ferri (1990)] and [Ferri and Bindemann (1995)]; stick-slip phenomena is the main topic investigated in the references [Awrejcewicz and Delfs (1990a); Awrejcewicz and Delfs (1990b); Baumberger et. al. (1995); Ionescu and Paumier (1993); Pratt and Williams (1981)] and [Stelter (1992)]. The study of friction may be based upon analytical calculation of solutions [Capecchi and Vestroni (1995)]. Some works describe experiments, identification and modelling of friction [Dowell and Schwartz (1983a); Dowell and Schwartz (1983b)] and [Tomlinson and Chen (1996)]. Numerical experiments have been made by many authors using classical numerical schemes [Stewart (1996); Stewart and Trinkle (1996)] and [Stewart and Trinkle (1997)]. Chaotic behaviour have been exhibited by nonlinear models including friction [Chua et. al.