## 1 Introduction
[PERSON] et al. [PERSON] et al. (2016) studied the dynamic behavior of rotor-SFD systems with cubic terms using the incremental harmonic balance method (IHB), identifying secondary Hopf bifurcations in second-order resonance regions under specific combinations of SFD centering spring stiffness and nonlinear stiffness parameters. Asymmetric SFD parameters significantly expanded unstable solution regions. [PERSON] et al. [PERSON] et al. (2016) established equations of motion for rotor systems with floating ring bearings using the transfer matrix method, analyzing stability trends under unbalanced forces through Poincare maps, frequency spectra, and bifurcation diagrams. In practical engineering applications, rotor systems are typically mounted on moving bases, subjected to additional excitation from base motion beyond rotational excitation. This configuration significantly complicates the dynamic behavior of nonlinear rotor systems, for which researchers have conducted extensive investigations. [PERSON] and [PERSON] [PERSON] and [PERSON] (2016) analyzed the dynamic characteristics of single-disk rotor systems with elastic supports under coupled excitation from mass unbalance and base motion. It demonstrated that under both linear and cubic nonlinear elastic support conditions, the coupling between base harmonic translation or harmonic rotation about the translational axis and unbalanced forces generates periodic and quasi-periodic motions. [PERSON] et al. [PERSON] et al. (2016) investigated rotor-fluid hydrodynamic bearing systems, revealing that the coupling between base harmonic rotation and mass unbalance produces various dynamic responses, including periodic, quasi-periodic, and chaotic motions. [PERSON] and [PERSON] [18; 19] utilized an Euler beam model and harmonic balance method to investigate base motion effects on two specialized rotor systems (cracked rotors and gear-coupled rotors) and revealed their vibration response characteristics and stability patterns. [PERSON] et al. [20; 21; 22; 23] employed Newmark-HHT numerical integration to investigate the dynamics of rotor systems under base motion excitation with various SFD configurations (\(\pi\)-film, full-film, with/without fluid inertia, with/without static eccentricity of the journal) and revealed that base harmonic translation induces quasi-periodic motions, double-frequency vibrations, and combination frequency responses between excitation and base harmonic frequencies. As the frequency of base harmonic translation increases, system motion evolves from periodic to quasi-periodic and ultimately to chaotic motion, independent of SFD centering condition. [PERSON] [24] developed a six-degree-of-freedom finite element model incorporating axial translational and rotational displacements for rotor-fluid bearing-support systems. Using Floquet theory and the Newmark method, the coupling effects between mass unbalance and base harmonic motion were analyzed. The results revealed that system instability under unidirectional rotational harmonic excitation stems from single-frequency parametric excitation, and pitching and yawing motions generated more complex instability regions compared to rolling motion. Under uniaxial base harmonic excitation, magnitude and phase angle of mass unbalance significantly affected system stability characteristics. [PERSON] [25] investigated the parametric stability of flexible rotor-magnetic bearing systems under periodic base motion using [PERSON]'s method and demonstrated that multiple control laws maintain system stability under base rolling, pitching, and yawing motions. In summary, although existing studies have explored the complex nonlinear dynamic characteristics of nonlinear rotor systems under dual excitation from base harmonic motion and unbalanced forces, research on nonlinear behaviors such as bistable phenomena in rotor systems with SFDs under base motion excitation requires further investigation.