Vibration of cracked shafts in bending

Cracked rotating shafts exhibit a certain particular dynamic response due to the local flexibility of the cracked section. In this response, most of the features of the response of a shaft with dissimilar moments of inertia can be identified. Moreover, the non-linear behavior of the closing crack introduces the characteristics of non-linear systems. For many practical applications, the system can be considered bi-linear and analytical methods can be applied. A de Laval rotor with an open crack is investigated by way of application of the theory of shafts with dissimilar moments of inertia. Furthermore, analytical solutions are obtained for the closing crack under the assumption of large static deflections, a situation common in turbomachinery. Finally, a solution is developed for the case in which the local flexibility function is found experimentally.