Analysis of Chaotic Response of Frenkel-Kontorova-Tomlinson Model

Abstract

The Frenkel-Kontorova-Tomlinson (FKT) model represents mechanical systems in which the atomic smooth surfaces of two bodies slide against each other. The model is very sensitive to changes of the system parameters, and ranges from simple stable harmonic to chaotic solutions. The design of the model between two bodies for the dynamic problem, following the network method rules, is explained with precision and run on standard electrical circuit simulation software. It provides the phase diagrams of atom displacement for each atom and the total friction force by the summation of all the atom displacements. This article is focused on studying the effect of the selected time step on the result and in the lack of sensitivity of Lyapunov exponents to assess chaotic behaviour.

Calculation and AFM Experimental Research on Slip Friction for Unlubricated Spherical Contact with Roughness Effect

“…In 1929, Tomlinson first proposed the molecular interaction theory of friction, according to which the cause of friction is the energy loss due to the intermolecular forces in the sliding process. With the gradual understanding of the phononic and electronic mechanisms, many energy dissipation friction models have been proposed, such as the Frenkel-Kontorova-Tomlinson model [2], Prandtl-Tomlinson model [3], Cobblestone Oscillator model [4], and so on.…”