The harmonic balance method with arc-length continuation in rotor/stator contact problems

There are a variety of abnormal running conditions in rotating machinery which lead to rotor/stator interaction dynamics which, in turn, can cause a rich mixture of effects associated with rub-related phenomena. These effects manifest themselves in the occurrence of multiple solutions for steady-state vibration response scenarios, including amplitude jumps during rotor acceleration, and vibration responses at different/multiple frequencies of excitation forces such as imbalance. This paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non-linear system under periodic excitation. The algorithm also calculates the stability of the periodic solutions found, marks turning and bifurcation points, and follows a solution branch over varying system parameters via arc-length continuation.