Stick-mode duration of a dry-friction oscillator with an uncertain model Roberta Lima a,n , Rubens Sampaio a a PUC-Rio, Department of Mechanical Engineering, Rua Marquês de Sao Vicente, 225, Gávea, 22451-900 RJ, Brazil article info Article history: Received 19 February 2015 Received in revised form 27 April 2015 Accepted 9 May 2015 Handling Editor: L.N. Virgin abstract 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. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction The motivation for exploring the different aspects of friction must have had its origin in solving practical problems. Friction is not a new subject. It had been a topic of technological attention long before the dawn of science, and it is still an important topic in science and engineering today [1–5]. Study of oscillatory conditions in dry friction systems has practical significance for providing protection against vibrations, seismic isolation, reduction of noise, and friction-induced vibration, etc. [6,7]. The nature of dynamic friction forces developed between bodies in contact is extremely complex and affected by many factors: the constitution of the interface, inertia and thermal effects, roughness of the contacting surfaces, history of loadings, the presence of lubricants, and many others [8–11]. Besides this, the stick–slip vibrations are self-sustained oscillations induced by dry friction [12] and since the friction can be characterized into two qualitatively different parts (kinetic and static frictions) with a non-smooth transition, the resulting motion also has a non-smooth behavior [13–17]. Two qualitatively different modes, the stick- and slip-modes, characterize the response of a dry-friction oscillator. We call stick when the relative velocity between the bodies in contact is null in a time-interval and we call slip if the relative velocity is non-zero, or zero in isolated points. As these two modes have a non-smooth transition between them, stick–slip systems belong to the class of non-smooth systems, such as systems with stops, impacts, and hysteresis [18–22]. The interest of analyzing the stick–slip dynamics is reflected by the increasing amount of research in this area (see for instance [23–26,20,27–29]). The friction non-smooth behavior associated with the absence of a universally accepted friction model Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration http://dx.doi.org/10.1016/j.jsv.2015.05.015 0022-460X/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: roberta_10_lima@hotmail.com (R. Lima), rsampaio@puc-rio.br (R. Sampaio). Journal of Sound and Vibration ] (]]]]) ]]]–]]] Please cite this article as: R. Lima, & R. Sampaio, Stick-mode duration of a dry-friction oscillator with an uncertain model, Journal of Sound and Vibration (2015), http://dx.doi.org/10.1016/j.jsv.2015.05.015i