Instability and friction

Quoc Son Nguyen

doi:10.1016/S1631-0721(03)00020-2

Instability and friction
[Instabilité et frottement]

Quoc Son Nguyen ¹

¹ Laboratoire de mécanique des solides, CNRS-UMR7649, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 99-112.

Résumé
Abstract

On présente dans cette Note une synthèse des résultats de la littérature sur l'analyse de stabilité des solides sous contact unilatéral avec frottement de Coulomb. Le problème de contact frottant d'un solide élastique avec un obstacle fixe ou mobile est examiné. La possibilité d'instabilité par divergence et la recherche d'un critère de stabilité statique d'un équilibre sont examinées dans le cas d'un obstacle fixe. La possibilité d'instabilité par flottement est ensuite discutée pour un équilibre résultant d'un glissement stationnaire avec un obstacle mobile. La solution de glissement stationnaire est dynamiquement instable par flottement et conduit à une réponse dynamique qui peut être chaotique ou périodique. En particulier, la réponse dynamique génère des ondes d'adhérence–glissement–séparation sur la surface de contact d'une façon comparable aux ondes de Schallamach en statique. Des exemples et des résultats récents de la littérature sont rapportés. Quelques problèmes de vibration et d'émission acoustique induites par le frottement, comme le crissement des freins par exemple, peuvent être interprétés dans cet esprit.

A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick–slip–separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of friction-induced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit.

Reçu le : 2002-12-02
Accepté le : 2002-12-18
Publié le : 2003-01-01

DOI : 10.1016/S1631-0721(03)00020-2

Keywords: Friction, Unilateral contact, Instability, Stick–slip–separation waves
Mots-clés : Frottement, Contact unilatéral, Instabilité, Ondes adhérence–glissement–séparation

Affiliations des auteurs :

Quoc Son Nguyen ¹

¹ Laboratoire de mécanique des solides, CNRS-UMR7649, École polytechnique, 91128 Palaiseau cedex, France

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Quoc Son Nguyen. Instability and friction. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 99-112. doi : 10.1016/S1631-0721(03)00020-2. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00020-2/

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