Fatigue cracking of the rotor shaft is an important fault observed in rotating machinery of key industry, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The four-th order Runge-Kutta method and ten-th order CFE-Euler (Continued Fraction Expansion-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by using bifurcation diagram, Poincare map and rotor trajectory diagram. The results show that the rotor system displays chaotic, quasi-periodic and periodic motions as the fractional order increases. It is also found that the imbalance eccentricity level, crack depth, rotational speed, fractional damping and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system.

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