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Register a new userDetecting singular weak-dissipation limit for flutter onset in reversible systems
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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 Pfluger 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 Pfluger 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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This work demonstrates preliminary results on energy harvesting from a linearly stable flutter-type system with circulatory friction forces. Harmonic external forcing is applied to study the energy flow in the steady sliding configuration. In certain parameter ranges negative excitation work is observed where the external forcing allows to pull part of the friction energy out of the system and thus makes energy harvesting possible. Studies reveal that this behavior is largely independent of the flutter point and thus that it is primarily controlled by the excitation. Contrary to existing energy harvesting approaches for such systems, this approach uses external forcing in the linearly stable regime of the oscillator which allows to control vibrations and harvest energy on demand.
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