Bifurcation analysis of coupled lateral/torsional vibrations of rotor systems

This paper presents a numerical method to analyze the bifurcation of coupled lateral/torsional vibrations of rotor systems. Based on a Hamiltonian approach, a three degree-of-freedom dynamic model of a rotor is derived. Nonlinear ordinary differential equations are derived from the dynamic model. The stability of the equilibrium and linear normal modes (LNMs) are analyzed using a linearized matrix of the system equation. For bifurcation analysis of the periodic orbits, a nonlinear normal modes (NNMs) computation algorithm is performed using multiple shooting methods and pseudo-arclength continuation. Multiple shooting points are continued from LNMs near equilibrium, bifurcation points of the NNMs are detected from the stability change of the periodic orbits during the continuation. The proposed stability analysis, an NNMs computation of coupled lateral/torsional vibration, is demonstrated using two different rotor models: a system with strong eccentricity, and a system with weak eccentricity. •Derivation of nonlinear ODE of coupled lateral/torsional vibration of rotor.•Bifurcation analysis of equilibrium is performed using a linearization technique.•Bifurcation analyses of periodic solutions using numerical continuation of NNMs.•Unstable self-excited vibrations with unsynchronized rotating speeds.