On Nonlinear Normal Modes of Systems With Internal Resonance

[+] Author and Article Information
A. H. Nayfeh, C. Chin

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219

S. A. Nayfeh

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Vib. Acoust 118(3), 340-345 (Jul 01, 1996) (6 pages) doi:10.1115/1.2888188 History: Received September 01, 1993; Revised June 01, 1994; Online February 26, 2008


A complex-variable invariant-manifold approach is used to construct the normal modes of weakly nonlinear discrete systems with cubic geometric nonlinearities and either a one-to-one or a three-to-one internal resonance. The nonlinear mode shapes are assumed to be slightly curved four-dimensional manifolds tangent to the linear eigenspaces of the two modes involved in the internal resonance at the equilibrium position. The dynamics on these manifolds is governed by three first-order autonomous equations. In contrast with the case of no internal resonance, the number of nonlinear normal modes may be more than the number of linear normal modes. Bifurcations of the calculated nonlinear normal modes are investigated.

Copyright © 1996 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In