Dry Friction in the Frenkel-Kontorova-Tomlinson Model: Dynamical Properties

TL;DR

This paper studies wearless friction in the Frenkel-Kontorova-Tomlinson model, analyzing how kinetic friction varies with sliding speed and interaction strength, revealing complex resonances, chaos, bistability, and soliton interactions.

Contribution

It introduces a detailed analysis of kinetic friction in the model for constant sliding speeds, including numerical and analytical results on phonon resonances and chaotic behavior.

Findings

Kinetic friction exhibits structures due to phonon resonances.

Increasing interaction strength leads to chaotic sliding states.

Discovery of bistabilities and soliton interactions in the model.

Abstract

Wearless friction is investigated in a simple mechanical model called Frenkel-Kontorova-Tomlinson model. We have introduced this model in [Phys. Rev. B, Vol. 53, 7539 (1996)] where the static friction has already been considered. Here the model is treated for constant sliding speed. The kinetic friction is calculated numerically as well as analytically. As a function of the sliding velocity it shows many structures which can be understood by varies kinds of phonon resonances (normal, superharmonic and parametric) caused by the so-called "washboard wave". For increasing interaction strength the regular motion becomes chaotic (fluid-sliding state). The fluid sliding state is mainly determined by the density of decay channels of m washboard waves into n phonons. We also find strong bistabilities and coherent motions with superimposed dark envelope solitons which interact nondestructively.