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

## TL;DR

This paper introduces an experimental setup to study the transition between classical and reversible Hopf bifurcations in nonconservative systems, confirming the Whitney umbrella singularity's role in dissipation-induced instabilities.

## Contribution

It provides the first laboratory demonstration of the singular interface between classical and reversible bifurcations in a viscoelastic system, validating theoretical predictions.

## Key findings

- High sensitivity of bifurcation onset to damping ratios
- Experimental confirmation of Whitney umbrella singularity
- Discontinuities in dissipation-induced instabilities

## 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 Pfl\"uger 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 Pfl\"uger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.