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

作者：Kirillov Oleg N^*

来源：Physics Letters A, 2009, 373(10): 940-945.

DOI：10.1016/j.physleta.2009.01.013

• Acoustics of friction
• Rotating continua
• Gyroscopic system
• Indefinite damping
• Flutter
• Parametric resonance
• Non-conservative positional forces
• Dissipation-induced instabilities
• Diabolical point
• Exceptional point

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.

• 出版日期2009-3-2