Flutter instability in elastic structures

Flutter instability in elastic structures

Davide Bigoni, Francesco Dal Corso, Andrea Piccolroaz, Diego Misseroni, Giovanni Noselli

Abstract. Flutter instability caused by follower loads has become a reality after the invention of the “freely-rotating wheel device” by Bigoni and Noselli, of the “flutter machine”, and of the device to generate Reut-type loads. Further research has proven that flutter instability, Hopf bifurcation, dissipation instabilities, and the Ziegler paradox are all possible in conservative systems, thus disproving an erroneous belief continuing since at least 50 years. Finally, a new type of flutter instability has been addressed, generated by the “fusion” of two structures which are separately stable, but become unstable when joined together. The analysis of instability involves here the treatment of a discontinuity in the curvature of a constraint.

Keywords
Flutter, Hopf Bifurcation, Non-Holonomic Systems

Published online 11/1/2023, 4 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Davide Bigoni, Francesco Dal Corso, Andrea Piccolroaz, Diego Misseroni, Giovanni Noselli, Flutter instability in elastic structures, Materials Research Proceedings, Vol. 37, pp 345-348, 2023

DOI: https://doi.org/10.21741/9781644902813-76

The article was published as article 76 of the book Aeronautics and Astronautics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] D. Bigoni and G. Noselli. Experimental evidence of flutter and divergence instabilities induced by dry friction. J. Mech. Phys. Solids, 59 (2011), 2208-2226. https://doi.org/10.1016/j.jmps.2011.05.007
[2] M. Tommasini, O. Kirillov, D. Misseroni, D. Bigoni. The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation, J. Mech. Phys. Solids 91 (2016), 204-215. https://doi.org/10.1016/j.jmps.2016.03.011
[3] D. Bigoni, O. Kirillov, D. Misseroni, G. Noselli, M. Tommasini. Flutter and divergence instability in the Pfluger column: Experimental evidence of the Ziegler destabilization paradox, J. Mech. Phys. Solids 116 (2018), 99-116. https://doi.org/10.1016/j.jmps.2018.03.024
[4] D. Bigoni, D. Misseroni. Structures loaded with a force acting along a fixed straight line, or the “Reut’s column” problem, J. Mech. Phys. Solids 134 (2020), 103741. https://doi.org/10.1016/j.jmps.2019.103741
[5] A. Cazzolli, F. Dal Corso, D. Bigoni. Non-holonomic constraints inducing flutter instability in structures under conservative loadings, J. Mech. Phys. Solids 138 (2020), 103919. https://doi.org/10.1016/j.jmps.2020.103919
[6] M. Rossi, A. Piccolroaz, D. Bigoni. Fusion of two stable elastic structures resulting in an unstable system, J. Mech. Phys. Solids 173 (2023), 105201. https://doi.org/10.1016/j.jmps.2023.105201
[7] H. Ziegler. Principles of structural stability, Birkhäuser, Basel und Stuttgart (1977). https://doi.org/10.1007/978-3-0348-5912-7
[8] W.T. Koiter.Unrealistic follower forces, J. Sound Vib. 194 (1996), 636–638. https://doi.org/10.1006/jsvi.1996.0383