Multi-dimensional harmonic balance applied to rotor dynamics

The multi-frequency dynamical behavior is a feature of many technical systems. Multiple shaft rotating machinery, subject to simultaneous unbalances spinning at different speeds is a particular case of such systems. Common methods of steady state solution are not valid when the addressed systems have non-linear properties. This study presents a generalized version of harmonic balance coupled with arc-length continuation, developed in order to study non-linear responses of modified Jeffcott rotor system subject to multiple unbalances. Numerically, the non-linear terms are taken into account via an AFT (alternating frequency-time domain) procedure, involving multi-dimensional FFT. An improvement to the AFT approach is proposed. The example addressed in this paper is a modified Jeffcott rotor with piece-wise radial stiffness.