In this study, a qualitative analysis of a transverse vibration of a rotor system
with a crack that grows at an angle of 45 degrees toward the axis of the shaft is
presented. Based on the assumption that the bending stiffness of the shaft changes
synchronously with the opening / closing behavior of the crack caused by the
torsional vibration of the shaft, the equation of motion of a simple rotor system
with a shaft having a slant crack is represented by a differential equation with
parametric excitation in fixed coordinate system rotating at the operation speed of
the rotor. Finally, it is shown by the solution that the steady-state response of the
rotor system with a slant crack on its shaft induced by imbalance contains the
frequencies represented by