Bifurcation analysis of stick–slip vibration in a 2-DOF nonlinear dynamical system with dry friction

Xuechuan Wang, Xinjun Long, Xiaokui Yue, Honghua Dai, Satya N. Atluri

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper describes a new approach to study the nonlinear dynamical behaviors of a belt-driven two-coupled friction oscillator. First, using Buckingham's π theorem, several dimensionless and physically meaningful parameters are derived. Their relationships with the steady state responses of the system are revealed through numerical simulations. Then a new mapping tool named as sticking phase plot is developed to record the transition process of stick–slip motion. It intuitively shows how bifurcation occurs in sticking region and transforms the dynamical responses. The bifurcation diagrams of the system are obtained by sweeping the dimensionless parameters. Some extraordinary bifurcation phenomena are observed in this system. By using sticking phase plot, it is found that the bifurcations can be broadly divided into four main categories: the Border-Collision Bifurcation, the Grazing-Sliding Bifurcation, the Multi-Sliding Bifurcation, and the Fixed-Point Bifurcation. New nonlinear phenomena are found herein, including chaos caused by the Border-Collision Bifurcation and the Sliding Bifurcations. The local and the global changes caused by the Fixed-Point bifurcation are also observed. In numerical simulation, we adopted the LVIM method proposed by the authors, which can be used to integrate non-smooth systems very accurately and efficiently.

Original languageEnglish
Article number106475
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Aug 2022


  • Bifurcations and chaos
  • Dry friction
  • Sticking phase plot
  • Stick–slip vibration


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