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Abstract
The presence of a crack in a structural member introduces a local flexibility that affects its vibration response. Moreover, the crack will open and close in time depending on the rotation and vibration amplitude. In this case the system is nonlinear. Furthermore, if general motion is considered, the local stiffness matrix description of the cracked section of the shaft leads to a coupled system, while for an uncracked shaft the system is decoupled. This means that the crack introduces new harmonics in the spectrum. In fact, in addition to the second harmonic of rotation and the subharmonic of the critical speed, two more families of harmonics are observed:
1. (1) higher harmonics of the rotating speed due to the nonlinearity of the closing crack, and
2. (2) longitudinal and torsional harmonics are present in the start-up lateral vibration spectrum due to the coupling.
Over 500 papers on the subject were published in the past 10 yrs. A wealth of analytical, numerical and experimental investigations now exists. However, a consistent cracked bar vibration theory is yet to be developed. There are still many unanswered questions, especially in the area of closing cracks in rotating shafts.
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