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 underly 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 Poincaré 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 feature that was found in the experimental system, but not in the simulations with simple friction laws.
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Feeny et al. (1994) studied this question.