In this study, a novel model is developed to investigate the angular acceleration of the nonlinear misaligned rotor passing through the critical speeds under non-stationary operating conditions. The concerned rotor is modeled elastic with the effects of nonlinear inertia terms and flexible bearing. Nonlinear equations of motion are derived using the Lagrange method and solved with the finite element method. Effects of parameters such as shaft eccentricity, damping, and stiffness of the supports on the increase in the rotor angular speed passing through the critical speed are considered. The obtained results indicate that a small amount of eccentricity prevents exceeding the elastic critical speed of the rotor. According to the results, if the support parameters are not selected properly, the rotor will not even be able to pass its rigid critical speed.
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