Sensitivity of Sub-critical Mode-coupling Instabilities in Non-conservative Rotating Continua to Stiffness and Damping Modifications

Mode-coupling instability is a widely accepted mechanism for the onset of friction-induced vibrations in car brakes, wheel sets, paper calendars, to name a few. In the presence of damping, gyroscopic, and non-conservative positional forces the merging of modes is imperfect, that is two modes may come close together in the complex plane without collision and then diverge so that one of the modes becomes unstable. In non-conservative rotating continua that respect axial symmetry this movement of eigenvalues is very sensitive to the variation of parameters of the system. Our study reveals some general rules that govern sub-critical mode-coupling instabilities in non-conservative rotating continua to stiffness and damping modifications and provide useful insight for optimisation of such systems and interpretation of experimental results.