Slip-stick motion in harmonic oscillator chains subject to Coulomb friction

Slip-stick motion is an extremely common phenomenon that exists in systems as diverse as tectonic plates, door hinges, and AFM probes. An examination of a simple harmonic oscillator subject to Coulomb friction has uncovered an important non-dimensional number that governs slip-stick motion. In this simple model, the boundary between systems that undergo slip-stick motion and steady sliding has been identified by a critical value of this non-dimensional number as a function of damping ratio. The non-dimensional number was found using a non-dimensionalisation of a simple one degree-of-freedom system, however, it has been found to govern the slip-stick boundaries of more complex systems with any number of degrees-of-freedom.