## 1 Introduction
Conversely, nonlinear modeling approaches--increasingly prevalent in recent studies--enable analysis under extreme conditions such as sudden load shocks or significant speed variations [19; 20]. These methods involve time-step tracking of component positions through coupled solutions of motion equations and governing equations, followed by vibration behavior evaluation using modal analysis techniques (e.g., power spectrum analysis, bifurcation diagram and Poincare map) over defined intervals [21; 22]. The primary objective of these dynamic analyses is to quantitatively assess parameter effects on system performance and to optimize their design and adjustment, thereby preventing surface contact and component wear caused by rotor instabilities within bearing clearance space under actual operating conditions. The combined application of signal monitoring and processing techniques for precise frequency response characterization with dynamic stability analysis methods of mechanical systems, particularly journal bearings, has advanced significantly in recent years, as these signal processing approaches enable more accurate vibrational response analysis by filtering out erroneous data and random noise [23; 24]. [PERSON] et al. [25] investigated the enhancement of static and dynamic performance in hydrodynamic circular journal bearings through triangular surface texturing. Their study examined variations in texture depth, quantity, and spatial distribution to evaluate their effects on steady-state behavior and dynamic properties, including lubricant film stiffness and damping coefficients, with comparisons made to conventional smooth bearings. At a constant eccentricity ratio of 0.6, results demonstrated that minimal texture depth optimizes threshold stability speed and stiffness, while maximum damping occurs at greater depths. [PERSON] et al. [26] explored the application of textured journal bearings to minimize viscous lubricant losses and enhance energy efficiency in rotating machinery. Their investigation focused on circular journal bearings with spherical textures, demonstrating that reduced shear adhesion forces could significantly decrease operational heat generation. This thermal reduction improves bearing performance and overall machine efficiency. Also, their numerical results confirmed that textured bearings effectively diminish shear adhesive forces in rotating systems. [PERSON] and [PERSON] [27] subsequently examined how micro-grooves affect the lubrication performance of misaligned circular journal bearings with a rotating shaft. Their findings revealed that groove angular positioning critically influences bearing performance under misalignment conditions. Both load-bearing capability and friction force were found to increase proportionally with greater misalignment angles and higher aspect ratios. [PERSON] and [PERSON] [28] conducted a study examining the influence of spherical surface textures on the dynamic behavior of hole-entry hybrid spherical bearings. Their findings revealed that incorporating spherical micro-cavities on the bearing's inner surface enhances rotor stability. Additionally, fully textured bearings exhibited a notable increase in fluid film stiffness coefficients, whereas damping coefficients demonstrated a declining trend. Later, [PERSON] et al. [29] investigated partially textured circular journal bearings lubricated using micropolar and power-law lubricants. Their results demonstrated an improvement in load carrying capacity alongside a reduction in frictional forces, highlighting the benefits of surface texturing under non-Newtonian lubrication conditions. [PERSON] et al. [30] conducted a computational analysis examining the static performance of hydrodynamic circular journal bearings featuring cylindrical micro-textures and lubricated with micropolar fluids, while incorporating mass conservation principles. Their study employed the finite difference approximations to solve the modified Reynolds equation, integrating [PERSON]'s mass-preserving scheme.