A “flutter machine” is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.

Detecting singular weak-dissipation limit for flutter onset in reversible systems / Bigoni, Davide; Misseroni, Diego; Tommasini, Mirko; Kirillov, Oleg; Noselli, Giovanni. - In: PHYSICAL REVIEW. E. - ISSN 2470-0053. - 97:2(2018), pp. 1-15. [10.1103/PhysRevE.97.023003]

Detecting singular weak-dissipation limit for flutter onset in reversible systems

Diego Misseroni;Giovanni Noselli
2018

Abstract

A “flutter machine” is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.
97
2
1
15
023003
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.023003
https://arxiv.org/abs/1706.02377
Bigoni, Davide; Misseroni, Diego; Tommasini, Mirko; Kirillov, Oleg; Noselli, Giovanni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/86120
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