One type of troublesome friction-induced noise, common in brakes, clutches and mechanical seals, is high frequency chirp or squeal. The frequencies at which these noises and underlying vibrations occur typically range from around 1 kHz to more than 10 kHz. We have found that the essential physical ingredients needed to model this problem are two finite elastic systems coupled by friction and a distributed interfacial contact stiffness, transverse to the direction of sliding. The contact stiffness is associated with the roughness of the sliding surfaces and, sometimes, with the presence of wear particles within the contact. Our approach is to perform an eigenvalue analysis, using finite elements, of pairs of coupled sliding elastic rings. Due to the presence of friction, the stiffness matrix is asymmetric and mode coupling or mode splitting can occur. Typically ten per cent of the first forty or so vibratory modes are potentially unstable. Generally one or two of these appear as instabilities in the actual physical system being modeled. No stick-slip action needs to be invoked and these instabilities can occur with a single constant coefficient of friction.

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