On Friction-Induced Instabilities and Vibrations

Abstract : Some problems of friction-induced instabilities, vibrations and noise emissions are considered in this paper. The presentation is focussed on the possibility of flutter instability of the steady sliding equilibrium of an elastic solid in unilateral contact with a moving obstacle. The system of governing equations is given to obtain the steady sliding equilibrium and to discuss its stability. It is shown that the steady sliding equilibrium is generically unstable by flutter. This instability leads to a dynamic response which can be periodic or chaotic. Principal results of the literature are reported here. In the spirit of Hopf bifurcation, the existence problem of periodic solutions has been discussed in my research team for an academic problem of coaxial cylinders. It has been shown by a semi-analytical approach that an interesting family of these periodic solutions are stick-slip-separation waves propagating on the contact surface in a similar way as Schallamach waves in statics. The transition from a given position near equilibrium to the propagation of waves has been illustrated by a numerical approach using finite element simulations. Some phenomena of nonlinear vibration and noise emission in the daily life, such as brake squeal for example, can be discussed in this spirit.
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Vietnam Journal of Mathematics, Springer, 2004, 32, pp.105-119
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Quoc Son Nguyen. On Friction-Induced Instabilities and Vibrations. Vietnam Journal of Mathematics, Springer, 2004, 32, pp.105-119. 〈hal-01911134〉

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