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

Abstract

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.

Stability of general asymmetric-anisotropic rotors subject to harmonic follower force

“…This apparently supports Pei’s viewpoints, regarding Bolotin’s method and gyroscopic systems. (Ferfecki et al, 2019) used Floquet’s theory to examine the stability of general rotor model subject to self-excitation due material damping. (Filippi and Carrera, 2021), proposed 1D finite element method to investigate stability and transient behavior for general rotor model and validated the obtained results using 3D finite element procedure and data from literature.…”