Analysis of a rotordynamic system with anisotropy and nonlinearity using the Floquet theory and the method of normal forms

The system under analysis is composed of an asymmetric rotor, two asymmetric bearings and a nonlinear spring-damper system representing an annular gas seal. The anisotropy in the rotor stiffness introduces time-periodic coefficients in the equations of motion which lead to parametric excitation with the typical resonance effects. As the additional anisotropy in the bearings may increase the area of unsafe operation conditions, the impact of these two different sources of anisotropy on the stability of the trivial solution is investigated in detail by a numerical approach based on the Floquet theory. Further insight into the stability behavior in case of an unstable trivial solution is obtained by accounting for stiffness and damping nonlinearities due to the gas seal. In this nonlinear case, the stability of the periodic solutions is analyzed by the semi-analytical method of normal forms revealing the influence of individual system parameters. The results of the semi-analytical approximation are verified by numerical calculations showing good agreement