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Mathematical Problems in Engineering
Volume 2017, Article ID 1208563, 19 pages
https://doi.org/10.1155/2017/1208563
Research Article

On Dynamical Behavior of a Friction-Induced Oscillator with 2-DOF on a Speed-Varying Traveling Belt

School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China

Correspondence should be addressed to Jinjun Fan; moc.621@81jjf

Received 30 September 2016; Accepted 4 January 2017; Published 5 February 2017

Academic Editor: Stefano Lenci

Copyright © 2017 Jinjun Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamical behavior of a friction-induced oscillator with 2-DOF on a speed-varying belt is investigated by using the flow switchability theory of discontinuous dynamical systems. The mechanical model consists of two masses and a speed-varying traveling belt. Both of the masses on the traveling belt are connected with three linear springs and three dampers and are harmonically excited. Different domains and boundaries for such system are defined according to the friction discontinuity. Based on the above domains and boundaries, the analytical conditions of the passable motions, stick motions, and grazing motions for the friction-induced oscillator are obtained mathematically. An analytical prediction of periodic motions is performed through the mapping dynamics. With appropriate mapping structure, the simulations of the stick and nonstick motions in the two-degree friction-induced oscillator are illustrated for a better understanding of the motion complexity.