Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator

A. Cammarano*, T. L. Hill, S. A. Neild, D. J. Wagg

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

49 Citations (Scopus)
349 Downloads (Pure)


This paper considers the dynamic response of coupled, forced and lightly damped nonlinear oscillators with two degree-of-freedom. For these systems, backbone curves define the resonant peaks in the frequency-displacement plane and give valuable information on the prediction of the frequency response of the system. Previously, it has been shown that bifurcations can occur in the backbone curves. In this paper, we present an analytical method enabling the identification of the conditions under which such bifurcations occur. The method, based on second-order nonlinear normal forms, is also able to provide information on the nature of the bifurcations and how they affect the characteristics of the response. This approach is applied to a two-degree-of-freedom mass, spring, damper system with cubic hardening springs. We use the second-order normal form method to transform the system coordinates and identify which parameter values will lead to resonant interactions and bifurcations of the backbone curves. Furthermore, the relationship between the backbone curves and the complex dynamics of the forced system is shown.

Original languageEnglish
Pages (from-to)311-320
Number of pages10
JournalNonlinear Dynamics
Issue number1-2
Early online date22 Feb 2014
Publication statusPublished - Jul 2014


  • Backbone curve
  • Bifurcation
  • Nonlinear oscillator
  • Second-order normal form method


Dive into the research topics of 'Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator'. Together they form a unique fingerprint.

Cite this