Regular and chaotic dynamics of a rotational machine with a centrifugal governor

The dynamic behavior of a rotational machine with centrifugal governor whic h is subjected to two different forms of external disturbance is studied in this paper. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. A codimension one bifurc ation analysis for the autonomous system is carried out near the degenerate point. It is found that a Hopf bifurcation occurs in the system. The incre mental harmonic balance (IHB) method combined with the multi-variable Floqu et theory has been effectively applied to obtain the steady state responses of the three-dimensional nonautonomous system. Phase portraits, power spec tra, Poincare maps, and Lyapunov exponents are presented to observe periodi c, quasi-periodic and chaotic motions. (C) 1999 Elsevier Science Ltd. All r ights reserved.