Nonlinear analysis on coupled flexural and torsional vibrations of cracked rotor

A Jeffcott cracked rotor considering nonlinear influences of whirl speed was investigated.Three kinds of nonlinear dynamical models were established seperately,which are pure flexural vibration model of rigidly supported beam,coupled flexural and torsional vibrations model of beam supported on rigid base and coupled flexural and torsional vibrations model of beam supported on elastic bearings.The behaviors of bifurcation and chaos were analyzed.Numerical simulations demonstrate that a complex nonlinear phenomenon is presented on the bifurcation plots of flexural vibrations of three kinds of models when the flexural stiffness difference Δkη is fairly large.Periodic,quasi-periodic and chaotic motions appear alternately when the rotating speed is near to 2/3ωc.The bifurcation plot of flexural vibration of model 1 is similar to that of model 2.And model 3 has more complex nonlinear characteristic.The bifurcation plots of torsional vibration of model 2 and 3 are similar to those of flexural vibration.And their nonlinear characteristics are all the same too.The analyzed results are helpful to knowing more about the dynamic characteristics of cracked rotors.