Frictional Stick-Slip Dynamics in a Deformable Potential

Abstract

Frictional stick-slip dynamics is carefully studied theoretically and numerically in a model of one oscillator interacting with a nonsinusoidal substrate potential. We focus our attention on a class of parameterised one-site Remoissenet–Peyrard potential U RP(X, r), whose shape can be varied as a function of parameter r and which has the sine-wave shape as a particular case. The evolution of the static friction as a function of the deformable parameter r is calculated. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasiperiodic and chaotic states. On the other hand, and for a good selection of the parameter systems, the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of the motions strongly depends on the shape parameter r. However, the stick-slip phenomena can be observed for all values of the shape parameter r in the range | r | < 1. The analytical analysis of the dry friction reveals that the dynamics depends non-trivially on the shape parameter r. Thus, the variable periodic potential allows us to consider a variety of substrate potential shapes useful in the description of real physical systems.