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

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.
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]
File in questo prodotto:
File Dimensione Formato  
zIaG0r-bigoni2018.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.41 MB
Formato Adobe PDF
1.41 MB Adobe PDF   Visualizza/Apri
Detecting singular weak-dissipation.pdf

accesso aperto

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 675.72 kB
Formato Adobe PDF
675.72 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/255349
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
social impact