Investigating Nonlinear Vibration Behavior of Rotors with Asymmetry Shaft Considering Misalignment

In this paper, the nonlinear vibration behavior of a rotor with asymmetric shaft considering misalignment is studied. The system consists of a rectangular shaft and a disk which is connected to a motor through a flexible coupling. In order to consider higher order deformations, nonlinear Bernoulli beam is used for modeling the shaft. Gibbons’ equations are utilized to apply misaligned coupling forces. The equations of motion of the system are derived using the Lagrangian method and then discretized by the Rayleigh-Ritz method. In order to solve nonlinear equations and hence obtaining nonlinear responses, multiple scales method is used. The vibration behavior of the system near the resonance frequencies is studied by taking into account various parameters including unbalance forces and the effect of the asymmetry of cross section of the shaft. The analytical results are consistent with those of numerical method with a good accuracy. In addition, the effects of variations of the system parameters on the rotor vibration behavior have been shown graphically. In the end, the changes in the various parameters of the system and their effects on the rotor vibration response are discussed.