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Edge flutter of
long beams under follower loads
Emmanuel de Langre and Olivier Doaré |
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Vol. 10 (2015), No. 3, 283–297
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DOI: 10.2140/jomms.2015.10.283
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Abstract |
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The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not depend on the length. The asymptotic regime significantly differs from that of short beams: flutter prevails for all types of follower loads, and flutter is localised at the edge of the beam. An approximate solution using matched asymptotic expansion is proposed for the case of a semi-infinite beam. Using a local criterion based on the stability of waves, the characteristics of this regime as well as its range of application can be well predicted. These results are finally discussed in relation with cases of flow-induced instabilities of slender structures. |
Keywords
follower force, flutter instability, semi-infinite, matched
asymptotic expansion
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Milestones
Received: 28 December 2013
Revised: 3 November 2014
Accepted: 25 December 2014
Published: 26 August 2015
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Authors |
| Emmanuel de Langre | |
| Département de Mécanique LadHyX École Polytechnique 91128 Palaiseau France |
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| Olivier Doaré | |
| Unité de Mécanique ENSTA-Paristech 828 Boulevard des Maréchaux 91120 Palaiseau France |
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