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Bifurcation to Divergence and Flutter in Flow-induced Oscillations: An Infinite Dimensional Analysis

Holmes, Philip and Marsden, Jerrold (1978) Bifurcation to Divergence and Flutter in Flow-induced Oscillations: An Infinite Dimensional Analysis. Automatica, 14 (4). pp. 367-384. ISSN 0005-1098. doi:10.1016/0005-1098(78)90036-5.

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We outline the application of center manifold theory to a problem of flow-induced vibrations in which bifurcations occur under the action of control parameters. Using these techniques, the governing nonlinear partial differential equation (PDE) can be replaced locally by a vector field on a low dimensional manifold. The bifurcations thus detected, including ‘global’ bifurcations, yield a useful description of the qualitative dynamics of the original PDE.

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Additional Information:© 1978 Published by Elsevier Ltd. Received 22 August 1977; revised 18 January 1978. Available online 11 February 2003. The original version of this paper was presented at the 2nd IFAC Symposium on the Control of Distributed Parameter Systems which was held in Coventry, England, during June–July 1977. The published Proceedings of this IFAC Meeting may be ordered from: Pergamon Press Ltd., Headington Hill Hall, Oxford OX3 0BW, England. This paper was recommended for publication in revised form by associate editor P. Parks. This work was done with the financial support of the Science Research Council of the UK (PH) and the National Science Foundation of the U.S.A. and the Carnegie Foundation (JM). During part of the work PH held a research fellowship at the Institute of Sound and Vibration Research. Southampton University. and JM was Visiting Professor at Heriot-Watt University, Edinburgh. Both authors would like to express their thanks to John Ball. Jack Carr, David Chillingworth, Brian Hassard, Carlos Mota-Soares. Tim Poston and Floris Takens for valuable discussions. comments and calculations.
Funding AgencyGrant Number
Science Research Council of the UKUNSPECIFIED
Carnegie FoundationUNSPECIFIED
Subject Keywords:Bifurcation; center manifold; control parameters; limit cycles; nonlinear equations; stability; vibrations
Issue or Number:4
Record Number:CaltechAUTHORS:20100811-080842986
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19383
Deposited By: Ruth Sustaita
Deposited On:13 Aug 2010 17:47
Last Modified:08 Nov 2021 23:51

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