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Self-oscillations of an elastic plate sliding over a smooth surface
Journal article   Peer reviewed

Self-oscillations of an elastic plate sliding over a smooth surface

A. I Leonov and A Srinivasan
International journal of engineering science, Vol.31(3), pp.453-473
03/01/1993
DOI: https://doi.org/10.1016/0020-7225(93)90018-P
Web of Science ID: WOS:A1993KN75400009

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Abstract

The 1-D problem of shear deformations of an elastic plate sliding over a smooth surface is analyzed analytically and numerically. The only source of dissipation in this model is the sliding friction at the interface. The non-monotonic characteristics of sliding friction proposed recently for rubber friction are used. The problem is then reduced to a recurrent set of algebraic equations and the analysis of this on a special phase diagram. In the region of self-oscillations, a complicated topological behavior of limit cycles is found—the sharpening of smooth initial conditions and the problem of non-uniqueness of solutions. The latter occurs when the dissipative forces are dominated. It is shown that in this case, the principle of choice based on the minimum of incremental dissipation corresponds to the inertialess descriptions of self-oscillations of the “relaxational type”. This is in good agreement with the exact numerical solution of the problem.

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