Bifurcation and chaos of a bladed overhung rotor with two disks supported on a centralized squeeze film damper

To analyze the stability of a bladed overhung rotor system with two disks supported on a centralized squeeze film damper,a blade-overhung rotor-CSFD model was formulated using the lumped mass method and the Lagrange approach.To reduce the scale of the nonlinear coupling system,a set of orthogonal transformations was employed to decouple one nodal diameter's dynamical equation of blades,which were coupled with the transverse vibration of the rotor.In this way,the original system with a 16+4n(n≥3) degree-of-freedom(DoF) was reduced to a system with only 24 DoF.Then the parametric excitation terms in the blade-overhang rotor-CSFD model were simplified in terms of periodic transformations.The coupling equations were numerically solved and the solutions were used to analyze the nonlinear feature of the system response in terms of the Poincare mapping,axes track curve,amplitude-frequency curve,bifurcation diagram,etc.Complicated nonlinear dynamic behaviors,such as period-doubling bifurcation,multi-period motion quasi-periodic motions,and chaos were observed.The higher stiffness of the retainer spring can enhance the stability of the system.