Using Floquet Theory in the Procedure for Investigation of the Motion Stability of a Rotor System Exhibiting Parametric and Self-Excited Vibration

The computational procedure for investigation vibration stability of a flexible rotor consisting of an asymmetric shaft, one disc, and supported by ball bearings is developed in this work. Lagrange equations of the second kind were used for derivation of the motion equation. The vibration response stability of the Jeffcott-like rotor was studied by means of eigenvalues of a transition matrix. Three different methods for approximation of the transition matrix have been investigated. The presented simulations are focused on studying the influence of parametric excitation produced by the shaft asymmetry and self-excitation vibration caused by the shaft material damping. The numerical results proved the applicability of the developed procedure, which has been verified by the direct integration of the motion equation.