Controlling chaos of nonlinear response in rotor containing a crack

We aim to study controlling nonlinear chaotic response in the Jeffcott rotor containing a crack in shaft. Considering the opening and closing of crack in rotation, we derive the motion equations of rotor. Based on the delay feedback control (DFC) method and perturbation of sinusoid periodic excitation, the novel chaos control scheme - sinusoid delay feedback (SDF) method - is presented. By choosing the appropriate coefficients, the chaotic response can be so controlled as to become gradually a periodic motion. By computing the largest Lyapunov exponent, the optimal control coefficients can be selected. From simulation results, it is shown that varying the weight coefficient and amplitude coefficient, the chaotic response of rotor containing a crack can be so controlled as to become gradually a synchronous, periodic-2 or periodic-4 motion.