Research on bifurcation characters of rotor system with SMA bearing

摘要

Based on Landau-Devonshire Shape Memory Alloy (SMA) model and Nitzsche-Breitbach-Elmar SMA model, the bifurcation characteristic of rotor-shape memory alloy bearings(SMAB) system was investigated in this paper. Heteronomous system was transformed into autonomous system in averaging method and Van der Pol transformation, and the existence of Hopf bifurcation was proved in theory. The concept of broadened set of equilibrium point was introduced to improve centre manifold method to be adapted to heteronomous system. The equation of the flow on the centre manifold of rotor-SMAB system was obtained, and the existence of transcritical bifurcation and supercritical pitchfork bifurcation was proved in theory. Finally the result in centre manifold method was compared with the one in averaging method. The comparison shows that the results of the two methods were both the parts of global dynamic characteristic of rotor-SMAB system, while centre manifold method can be applied to research bifurcation behavior in the case of more codimensions. It means that the two methods both have limitation, and global dynamic characteristic must be obtained in kinds of method.