Nonlinear Vibration Analysis of Asymmetric Rotor with Misaligned Coupling Using Timoshenko Beam Theory

In the present study, a proper analytical model is developed for investigating nonlinear vibration behavior of asymmetric and symmetric rotors under unbalanced and misalignment induced forces in rotating coordinates. The rotor is connected to a motor through an asymmetric coupling. For a more accurate vibration analysis, Timoshenko's beam theory is applied and for a better modeling of misaligned coupling forces, Gibbons’ equations are used. The equations of motion are discretized by Rayleigh-Ritz method and derived from Hamilton's principle, thereafter. According to this investigation, for asymmetric rotors as opposed to symmetric rotors, a frequency range is detected in which resonance and instability occurs. Also, the dynamic behaviors of the symmetric and asymmetric rotors are analyzed at the same rotational speed to indicate specifically the effects of different parameters on both rotors. For investigating the vibration behaviors of the rotors more accurately, their time-domain vibration responses are plotted and then their Fast Fourier Transform (FFT) are presented to determine the vibration frequencies of the rotors, so the effects of different parameters can be well observed. As a whole, in this study, the effects of each of the defects such as shaft asymmetry, misalignment, mass unbalance and also nonlinear terms are investigated on the dynamic behavior of the rotor system.