Influences of fractional order damping on nonlinear dynamics of cracked rotor

Nonlinear dynamics of cracked rotor system with fractional order damping is investigated with a response-dependent breathing crack model. The fourth order Runge-Kutta method and tenth order continued fraction expansion Euler (CFE-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 bifurcation diagram, Poincare map and rotor trajectory diagram. The results show that the rotor system gets chaotic, quasi-periodic and periodic as the fractional order increases. It is also found that the imbalance eccentricity level, crack depth, rotational speed, fractional damping and crack angle all exert considerable influence on the nonlinear behaviors of cracked rotor system.