Chaos in a forced dry-friction oscillator: Experiments and numerical modelling

Abstract

The chaotic dynamics of a harmonically forced spring-mass system with dry friction is studied experimentally and numerically. The friction in the experiment was designed to vary linearly with displacement. A one-dimensional single-humped map is shown to underlie the dynamics. Three friction laws are examined during the numerical modeling: the discontinuous Coulomb model, a continuous version of the Coulomb model, and a state-variable friction law. Using experimental Poincare maps, the qualitative features of the chaotic attractor in the three-dimensional phase space were discovered and used to evaluate the friction models. Each friction model produces the main qualitative features of the dynamics observed in the experiment. The state-variable friction law produces one features that was found in the experimental system, but not in the simulations with simple friction laws. © 1994 Academic Press Limited.