Stability analysis for transverse breathing cracks in rotor systems

• New breathing functions are adopted to model a cracked Jeffcott rotor.
• Unstable regions are detected in the dynamics of the cracked rotor.
• Three types of bifurcations are found in the unstable regions numerically.
• Damping has significant influence on the structures of the unstable regions.

Transverse breathing cracks have been considered a primary mode of damage in studies of rotordynamic systems. In this paper, a Jeffcott rotor with a transverse breathing crack is examined, and stability of the system is investigated by Floquet theory considering the crack depth and rotating speed. New breathing functions proposed in a recent publication are adopted to approximate the actual breathing mechanism of the crack. Unlike previous studies wherein stability diagrams without detailed information about the stable and unstable regimes of the motion have been provided, in this work we perform a detailed study of the corresponding eigenvalues of the cracked rotor in the complex plane, and the effect of damping on the instability regions has been investigated. Our study indicates that the unstable regions appear as the speed of the rotor approaches an integer fraction or an integer multiple of the critical speed of the rotor, whereas bifurcations are detected in certain unstable regimes. The results also shows damping has significant influence on the structures of instability regions.