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The first experimental evidence of the Ziegler destabilization paradox

Oleg Kirillov's picture

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.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.023003

https://www.sciencedirect.com/science/article/pii/S0022509618300784?via%...

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