Analysis of the stick-mode duration of dry-friction oscillators with a stochastic approach

Resumen

This paper analyzes the behavior of a stick-slip dry-friction oscillator considering the exis- tence of uncertainties in a friction parameter. The system studied is composed by a block 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. Solutions to the phase diagram of the case of belt with constant velocity are analytically developed. By numerical simulations, this simpler case is compared with different imposed non-smooth belt velocity configurations, from a deterministic and from a stochastic viewpoint. The focus of the paper is to determine the duration of the stick- and slip-mode parts of the trajectory through the phase diagram. In the stochastic analysis, the belt speed is modeled as a random process. Monte Carlo simulations are employed to compute the statistics of the response of the stochastic dry-friction oscillator. The variable of interest is the duration of the stick-mode of the trajectory.