The vibration of a multi-crack rotor

In this paper a mode of free vibrational analysis of multi-cracked rotor is presented. The cracks are assumed to be in the first mode of fracture, i.e. the opening mode. Based on the Timoshenko beam theory, the frequency equation can be constructed by assembling the transfer matrix of each segment of the multi-step and multi-cracked rotor, and then solve the frequencies as well as the corresponding mode shapes of the cracked rotor. The effects of both relative distances along axis and/or orientations of cracks are considered in free vibration analysis. An algorithm and numerical examples are included.