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Resonant frequency calculations using a hybrid perturbation-Galerkin techniqueA two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degrees of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.
Document ID
19920057312
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Geer, James F.
(New York, State University Binghamton, United States)
Andersen, Carl M.
(College of William and Mary Williamsburg, VA, United States)
Date Acquired
August 15, 2013
Publication Date
November 1, 1991
Publication Information
Publication: Applied Mechanics Reviews
Volume: 44
Issue: 11:00 PM
ISSN: 0003-6900
Subject Category
Physics (General)
Accession Number
92A39936
Funding Number(s)
CONTRACT_GRANT: NAS1-18605
Distribution Limits
Public
Copyright
Other

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