Subcritical flutter in the acoustics of friction of the spinning rotationally symmetric elastic continua

Linearized models of elastic bodies of revolution, spinning about their symmetrical axes, possess the eigenfrequency plots with respect to the rotational speed, which form a mesh with double semi-simple eigenfrequencies at the nodes. At contact with friction pads, the rotating continua, such as the singing wine glass or the squealing disc/drum brake, start to vibrate because of the subcritical flutter instability. In the present paper a sensitivity analysis of the spectral mesh is developed for the explicit predicting the onset of instability. The determining role of the Krein signature of the eigenvalues involved in the crossings as well as the key role of the indefinite damping and non-conservative positional forces is clarified in the development and localization of the subcritical flutter. It is established that even when the rotational symmetry is broken by the variation of the structure of the stiffness matrix and therefore the eigenvalues of the undamped gyroscopic system avoid crossings, its perturbation by the dissipative forces with the indefinite matrix can cause flutter instability in the subcritical region.