Dynamics of a 2-DOF dry friction system under two-frequency excitations

Gong Cheng, Jean W. Zu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the dynamics of a two-degree-of-freedom block-on-belt system subjected to both dry friction and external excitations is studied. The dry friction in the system follows the classical Coulomb's law, and the external excitations consist of two harmonic forces with different frequencies. In the study, a new two-dimensional (2-D) map is developed, which reduces the system without losing its essential dynamic features and greatly simplifies the investigation. On the basis of the 2-D map, bifurcation analysis and the computation of Poincaré sections and Lyapunov exponents can be carried out straightforwardly. Numerical simulations are performed, in which the proposed 2-D map is proved to be very effective and provide a powerful tool to understand the dynamical behavior of the system. Numerical results show that the system possesses rich dynamics characterized by periodic, quasi-periodic and chaotic attractors. Furthermore, it is found that the two-frequency excitation has significant influence on the dynamical behavior of the system.

Original languageEnglish
Pages (from-to)647-665
Number of pages19
JournalInternational Journal of Applied Mechanics
Volume1
Issue number4
DOIs
StatePublished - Dec 2009

Keywords

  • 2-D map
  • Bifurcation
  • Lyapunov exponent
  • Poincaré section
  • dry friction
  • dynamics
  • two-frequency excitation

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