Vol. 10, No. 3, 2015

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Edge flutter of long beams under follower loads

Emmanuel de Langre and Olivier Doaré

Vol. 10 (2015), No. 3, 283–297
DOI: 10.2140/jomms.2015.10.283

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.

follower force, flutter instability, semi-infinite, matched asymptotic expansion
Received: 28 December 2013
Revised: 3 November 2014
Accepted: 25 December 2014
Published: 26 August 2015
Emmanuel de Langre
Département de Mécanique
École Polytechnique
91128 Palaiseau
Olivier Doaré
Unité de Mécanique
828 Boulevard des Maréchaux
91120 Palaiseau