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

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 non-zero 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.

17 pages, 10 figures, typos corrected, refs added. Accepted to PRE

References in corpus (4)

• The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation
• Enhancement of the Benjamin-Feir instability with dissipation
• Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes
• Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics

Cited by in corpus (7)

• Flutter and divergence instability in the Pfluger column: experimental evidence of the Ziegler destabilization paradox
• Flutter instability in solids and structures, with a view on biomechanics and metamaterials
• Non-holonomic constraints inducing flutter insability in structures under conservative loadings
• Structures loaded with a force acting along a fixed straight line, or the "Reut's column problem"
• Flutter instability and Ziegler destabilization paradox for elastic rods subject to non-holonomic constraints
• From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory
• Finding the strongest stable weightless column with a follower load and relocatable concentrated masses