In the first part of this study, the dynamic behavior of a cracked rotating shaft with a rigid disk is analyzed, with an ideal and a nonideal motor, passing through its critical speed. The shaft contains a single transverse crack that is assumed to be either completely open or completely closed at any given time, depending on the curvature of the shaft at the cross section containing the crack. Flexible, damped supports and overhangs with a mass at one end are included. The supports are modeled with elastic springs and dashpots. The influence of gyroscopic moments of the disk (with an ideal motor) is investigated. For a nonideal motor, there is an interaction between the shaft and the motor.

Eccentricity of the disk, gravitational forces, and internal and external damping are included. The equations of motion and boundary conditions are derived by Hamilton's Principle. To eliminate the spatial dependence, the Extended Galerkin Method is applied. Longitudinal vibration, shear deformation and torsional vibration are neglected.

In the second part of this study, the vibration suppression of a cracked, simply supported, rotating shaft with a rigid disk is discussed, with an ideal and a nonideal motor, passing through the critical speed. The use of a flexible internal constraint is introduced to suppress the vibration. By activating this additional internal support, the shaft is prevented from passing its critical speed. Transient motions occur at the time of activation or deactivation of the constraint. The maximum displacement of the shaft during acceleration (run-up) or deceleration (coast-down) can be reduced significantly by appropriate application of this flexible internal support.