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


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
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