Dry-friction Oscillator Research Articles

A Detailed Study of the Low-Frequency Periodic Behavior of a Dry Friction Oscillator

This work examines the periodic stopping motion present in the low-frequency response of a dry friction oscillator, excited harmonically through a base spring. Piecewise linear solution methods are used to compare two simple friction models, to consider the effects of viscous damping, and to illustrate stability considerations. Seeding phenomena, particularly at degenerate frequency ratios, are noted. Finally, experimental results provide a means to assess the effectiveness of the simple friction models in predicting observed motion.

Chaos in a Forced Dry-Friction Oscillator: Experiments and Numerical Modelling

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.

Autocorrelation on symbol dynamics for a chaotic dry-friction oscillator

An autocorrelation function based on symbol dynamics is applied to a chaotic dry-friction oscillator to estimate the largest Lyapunov exponent. The friction problem is well suited for symbol dynamics since two distinct states of motion can be identified: sticking and slipping. In addition, the dynamics of the oscillator can be reduced to a non-invertible one-dimensional map, which has been studied in terms of binary symbol sequences. The study is done for an experimental oscillator and for a numerical model. The numerical result is compared to the Lyapunov exponent estimated from the continuous flow.