Flutter Instability of Circular Discs with Frictional Follower Loads

Untwisting the Campbell diagrams of weakly anisotropic rotor systems

“…1(f). This rather complicated behavior is difficult to predict and even to interpret as it was reported in the studies of numerous mechanical systems, see, e.g, [20,21,24,25,27,29,35,36,39,43,48]. The present work reveals that the untwisting of the Campbell diagrams is determined by a limited number of singular eigenvalue surfaces.…”

“…4. MacKay's eigenvalue cones and instability bubbles due to stiffness modification Modification of the stiffness matrix induced by the elastic support or by the stationary spring interacting with the rotating continua is typical in the models of rotating shafts [10,11], computer disc drives [20,21], circular saws [25,27,29], disc brakes [24,48], and turbine discs [39]. Assuming δ = 0 and ν = 0 in (11) we find that the eigenvalues of the system (5) with the stiffness modification κK either are pure imaginary (Reλ = 0) and form a conical surface in the (Ω, κ, Imλ)-space with the apex at the point (Ω 0 , 0, ω 0 ), Fig.…”

“…Interaction of waves with positive and negative energy is a well known mechanism of instability of the moving fluids and plasmas [15,18]; in rotor dynamics this yields flutter in the supercritical speed range, which is known as the mass and stiffness instabilities [24,39].…”

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

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Although both modal analysis and transient analysis of the nonlinear system [16,17] are the two widely accepted complementary methods in modern treatments of such problems, we will concentrate on the former in this paper.…”

“…Frequently, linearisation and discretisation of the models derived for the description of the mode-coupling instability in brakes yields a finite-dimensional circulatory system 0  x Ax  (1) where dot denotes time differentiation and A is a real non-symmetric matrix that is related to potential and non-conservative positional (or circulatory) forces [2,3,[11][12][13][14].…”