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

There are a variety of abnormal running conditions in rotating machinery wh ich lead to rotor/stator interaction dynamics which, in turn, can cause a r ich mixture of effects associated with rub-related phenomena. These effects manifest themselves in the occurrence of multiple solutions for steady sta te vibration response scenarios, including amplitude jumps during rotor acc eleration, and vibration responses at different/multiple frequencies of exc itation forces such as unbalance. This paper describes a numerical algorith m based on the harmonic balance method to calculate the periodic response o f a non-linear system under periodic excitation. The algorithm also calcula tes the stability of the periodic solutions found, marks turning and bifurc ation points, and follows a solution branch over varying system parameters via are-length continuation. (C) 2001 Academic Press.