The Stick-Slip Vibration and Bifurcation of a Vibro-Impact System with Dry Friction

Quanfu Gao, Xingxiao Cao*
School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

© 2014 Gao and Cao

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the 88 Anning West Road, Lanzhou, Postcard: 730070, China; Tel: 13659437212; E-mail:


In this paper, the periodic motion, bifurcation and chatter of two-degree-of-freedom vibratory system with dry friction and clearance were studied. Slip-stick motion and the impact of system motions were analyzed and numerical simulations were also carried out. The results showed that the system possesses rich dynamics characterized by periodic motion, stick-slip-impact motion, quasi-periodic motion and chaotic attractors, and the routs from periodic motions to chaos observed via Hof bifurcation or period-doubling bifurcation. Furthermore, it was found that there exists the chatter phenomena induced by dry friction in low frequency, and the windows of chaotic motion are broadened in the area of higher excitation frequencies as the dry friction increases.

Keywords: Chatter, Dry friction, Hopf bifurcation, Stick-slip, Vibro-Impact.