Analysis of the Stick-Mode Duration of Dry-Friction Oscillators R. Lima a,b,* , R. Sampaio a a Department of Mechanical Engineering, PUC-Rio, Rua Marquˆ es de Sao Vicente, 225, G´ avea, 22453-900, RJ, Brazil b Laboratoire de Modelisation et Simulation Multi Echelle, Equipe de Mecanique, Paris-Est, 5, Boulevard Descartes, 77454, Marne-la-Vallee, Cedex 2, France Abstract This paper analyzes the behavior of a stick-slip dry-friction oscillator composed by a block of mass m connected to a fixed support by a spring of stiffness k. 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 de- veloped. 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 finding the stick- and slip-mode parts of the trajectory through the phase diagram. In the stochastic analysis, the belt speed is considered uncertain and is modeled as random process. Monte Carlo simulations are employed to compute the statistics of the response of the stochastic differential equation of motion of the stick-slip dry-friction oscillator. The variable of interest is the duration of the stick-mode of the trajectory. Keywords: Friction-induced vibration, stick-slip, non-smooth system, nonlinear-dynamics, stochastic modeling. * Corresponding author Email addresses: roberta_10_lima@hotmail.com (R. Lima ), rsampaio@puc-rio.br (R. Sampaio) Preprint submitted to Journal of Sound and Vibrations December 18, 2013 Manuscript Click here to download Manuscript: JSV - Lima_Sampaio.pdf Click here to view linked References