Unfolding the conical zones of the dissipation-induced subcritical flutter for the rotationally symmetrical gyroscopic systems

TL;DR

This paper investigates how indefinite damping and non-conservative forces create conical zones of subcritical flutter in spinning elastic bodies, revealing that symmetry-breaking can promote rather than inhibit rotor oscillations.

Contribution

It uncovers the formation of conical domains of subcritical flutter due to damping and forces, explaining counterintuitive rotor behavior with a novel bifurcation analysis.

Findings

Indefinite damping creates conical flutter zones.

Non-conservative forces lead to Whitney umbrella bifurcations.

Symmetry-breaking can promote rotor oscillations.

Abstract

Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney's umbrellas when non-conservative positional forces are additionally taken into account. This explains why in contrast to the common intuition, but in agreement with experience, symmetry-breaking stiffness variation can promote subcritical friction-induced oscillations of the rotor rather than inhibit them.