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

The dynamic behavior of a rotational machine with centrifugal governor which 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 bifurcation analysis for the autonomous system is carried out near the degenerate point. It is found that a Hopf bifurcation occurs in the system. The incremental harmonic balance (IHB) method combined with the multi-variable Floquet theory has been effectively applied to obtain the steady state responses of the three-dimensional nonautonomous system. Phase portraits, power spectra, Poincare maps, and Lyapunov exponents are presented to observe periodic, quasi-periodic and chaotic motions.

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