0
RESEARCH PAPERS

An Application of the Poincaré Map to the Stability of Nonlinear Normal Modes

[+] Author and Article Information
L. A. Month

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

R. H. Rand

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y. 14853

J. Appl. Mech 47(3), 645-651 (Sep 01, 1980) (7 pages) doi:10.1115/1.3153747 History: Received September 01, 1979; Revised February 01, 1980; Online July 21, 2009

Abstract

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincaré map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincaré map approach succeeds.

Copyright © 1980 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

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