Coupled bending, longitudinal and torsional vibrations of a cracked rotor

The coupling between longitudinal, lateral and torsional vibrations is studied together for a rotating cracked shaft. These coupling mechanisms have been studied here with a response-dependent non-linear breathing crack model. Most of the earlier work on coupled vibrations due to crack has been either on stationary shaft or on rotating shaft with open crack model. The stiffness matrix of a Timoshenko beam element is modified to account for the effect of a crack and all the six degrees of freedom per node are considered. Coupled torsional–longitudinal vibrations for a cracked rotor that has not been reported earlier and coupled torsional–bending vibrations with a breathing crack model have been studied. An attempt has been made to reveal crack specific signatures by using additional external excitations. Since all the couplings are accounted, the excitation in one mode leads to an interaction between all the modes. This, coupled with the rotational effect of a cracked rotor and the non-linearities due to a breathing crack model introduces sum and difference frequencies in the response of cracked rotor. The co-existence of frequencies of other modes in the frequency spectra of a particular mode and the presence of sum and difference frequencies around the excitation frequencies and its harmonics could be useful indicators for crack diagnosis.