Edge flutter of long beams under follower loads

TL;DR

This paper investigates the linear instability of long beams under follower loads, revealing that for sufficiently long beams, flutter instability occurs at the edge regardless of load type, with an asymptotic analysis providing predictive insights.

Contribution

It introduces an asymptotic analysis for long beams under follower loads, showing flutter localization at the edge and independence from length, extending understanding of flow-induced instabilities.

Findings

Flutter dominates for all follower loads in long beams.

Instability is localized at the beam edge.

Asymptotic solutions accurately predict the instability regime.

Abstract

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 localized at the edge of the beam. An approximate solution using matched assymptotic 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.