Stability analysis of a rotor with crack and nonlinear stiffness by perturbation method

Abstract

Abstract The vibration of the cracked rotor differs greatly from that of the uncracked rotor, resulting in unstable phenomena. The nonlinear stiffness of the support is distinctly appeared in a rotor which operates at the high rotating speed. The equations of motion of the Jeffcott rotor were established to reflect the effect of crack and nonlinear stiffness of the support in a cracked rotor and those first approximate solutions were found by using the perturbation method. The stability evaluation of the first approximation system shows that the greater the crack parameter, the greater the instability and the pitchfork and double bifurcations occur. The occurrence of chaotic vibrations was evaluated with Lyapunov exponent and the existence of the chaotic vibration was analyzed with the fractal dimension in the rotor with the crack and the nonlinear stiffness.