In this paper, a methodology to analyze the nonlinear vibration of a Jeffcott rotor supported on a squeeze-film damper (SFD) with centering springs, which is widely used in high-speed rotating machines, is proposed using the incremental harmonic balance (IHB) method. In this paper, the IHB method is modified to analyze the dynamic behavior of rotor systems supported on fluid-film bearings, such as SFDs. The processing of the mass matrix, stiffness matrix, and linear force matrix proceeds in exactly the same way as in classical IHB. The nonlinear force generated in the oil film of the SFD is calculated using the alternating frequency/time method and the transformation matrix and incorporated into the computational processing of the classical IHB method. This calculation method is first proposed in this paper. Solutions computed using the proposed method are compared with solutions computed using numerical integration. The results are very close. The stability of the calculated solutions is determined using the Floquet theory. Based on this, frequency–response curves according to the change in various parameters are constructed. The proposed method can be effectively used to analyze the nonlinear vibration characteristics of rotor systems supported on fluid-film bearings, such as SFDs.
In this paper, the nonlinear vibration of a flexible rotor supported on squeeze-film dampers (SFDs) with centering springs is analyzed using the incremental harmonic balance (IHB) method, and bifurcation phenomena appeared in the resonance region are investigated. Complex nonlinear phenomena occur in this system due to the interaction of the fluid-film forces and the unbalance forces of the rotor in the SFD. Systems with these complex nonlinearities cannot be solved using the classical IHB methods. To overcome this problem, the classical IHB method and the alternating frequency/time (AFT) method are combined. The processing of linear matrices is performed in the same way as the classical IHB method, and only the processing of nonlinear force matrix caused by fluid–structure interaction is modified (application of transformation matrix). To prove the validity of the proposed method, the results calculated using the proposed method are compared with the results calculated using the Runge–Kutta method and the results presented in reference. Then, frequency response curves according to changes in bearing parameter [Formula: see text], gravity parameter [Formula: see text], stiffness ratio [Formula: see text], mass ratio [Formula: see text], and unbalance parameter [Formula: see text] are constructed. Stability and bifurcation analyses of the calculated solution are performed using the Floquet theory. The proposed method can be effectively applied to the nonlinear vibration analysis of rotor systems supported on fluid-film bearings.
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