Stick-mode duration of a dry-friction oscillator with an uncertain model

This paper investigates the dynamics of a simple dry-friction oscillator which is composed of a block, modeled as a particle, connected to a fixed support by a spring. The block moves over a continuous belt that is driven by rollers. The frictional force between the block and the belt is modeled as a Coulomb friction. Due to this friction model, the resulting motion of the block can be characterized into two qualitatively different modes, the stick- and slip-modes, with a non-smooth transition between them. The focus of the paper is to quantify the percent of time in which the block stays in the stick-mode for different models of periodic belt velocity and for different values of the friction coefficient. Continuous, discontinuous, and random models of belt velocity were considered. The objective is to compare their influence in the duration of the stick-mode. The time of stick represents the fraction of time that the oscillator sticks, it can be viewed as the probability of a biased-coin problem: stick is head and slip is tail.