Breathing response in a statically indeterminate cracked rotor

A new iterative-analytical approach to determining the static behaviour of a cracked rotor has been developed and applied to a statically indeterminate model. The model subjects the cracked shaft to out-of-plane bending due the inclusion of an offset dynamic force. The interaction between fixed supports and the variable shaft stiffness caused by a breathing crack make the model analytically unsolvable. The presented iterative algorithm for determining the breathing state of the crack makes the model analytically solvable for the support reactions and the elastic deflections. The algorithm rapidly converges, requiring typically fewer than 4 iterations to achieve stable results. The breathing response for a particular set of model parameters has been evaluated and is presented.