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, D.; Misseroni, D.; Tommasini, M.; Kirillov, O. N.; Noselli, G.. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 97:2(2018), pp. 023003.1-023003.15. [10.1103/PhysRevE.97.023003]

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

Bigoni D.;Misseroni D.;Tommasini M.;Noselli G.
2018-01-01

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.
2018
2
Bigoni, D.; Misseroni, D.; Tommasini, M.; Kirillov, O. N.; Noselli, G.
Detecting singular weak-dissipation limit for flutter onset in reversible systems / Bigoni, D.; Misseroni, D.; Tommasini, M.; Kirillov, O. N.; Noselli, G.. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 97:2(2018), pp. 023003.1-023003.15. [10.1103/PhysRevE.97.023003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/255349
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