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

Davide Bigoni, Diego Misseroni, and Mirko Tommasini

Oleg N. Kirillov*

Giovanni Noselli

  • University of Trento, via Mesiano 77, 38123 Trento, Italy

  • Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom

  • SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy

  • *Electronic address: oleg.kirillov@northumbria.ac.uk
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Phys. Rev. E 97, 023003 – Published 20 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.023003

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.

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Phys. Rev. E 97, 023003– Published 20 February, 2018
  • Received 7 June 2017
  • Revised 4 January 2018
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