## 1 Introduction
Recent FSI research delves deeper, including the development of efficient 3D nonlinear finite element models for predicting stick-slip torsional vibration [36]; analyzing the stability boundaries of rotating pipes under combined internal and external flow using analytical/semi-analytical coupled models [23]; utilizing axial-torsional coupling models to analyze the different effects of feed rate and rotational speed on vibration complexity [37]; and analyzing the combined effects of mud flow rate, WOB, and rotational speed on vibration and stability through finite element models considering nonlinearities and mud effects [38]. Stability analysis under fluctuating loads also indicates that fluctuating WOB and related parameters can drive parametric resonance instability [39]. The rheology of existing drilling fluids has limited effectiveness in suppressing vertical chatter, and their shear-thinning behavior may conflict with vibration damping requirements [40]. [PERSON] et al. specifically modeled non-Newtonian fluids using the Quemada model to assess their impact on hydraulic forces [41]. However, considering the dynamic pressure drop of non-Newtonian fluids significantly alters the predicted critical rotational speeds for lateral vibration, especially under specific operating conditions, suggesting this factor should be included when formulating vibration avoidance strategies [42]. Further research indicates that the optimal combination of drilling fluid rheological parameters differs for suppressing different types of vibration (axial, lateral, torsional), providing a theoretical basis for vibration control through drilling fluid optimization [43]. The frictional energy dissipation between the drill string and wellbore wall, as a non-productive energy expenditure, should be minimized during the drilling process. However, related research is scarce. Simultaneously, many analyses tend to simplify the drill string as a slender rotating beam, which, to some extent, neglecting its complex three-dimensional structural dynamic characteristics. This simplification is challenged by models like those from [PERSON] et al., which use geometrically exact rod theory, and [PERSON] et al., who employ 3D beam finite elements for curved wells. [PERSON] et al. also emphasized that drill strings are inherently distributed systems and simple lumped models fail to capture their rich dynamics [4; 10; 13]. Furthermore, in-depth research remains insufficient regarding the highly nonlinear, two-way fluid-structure coupling problem under transient conditions, particularly in scenarios involving small-diameter horizontal wells where drill string-wellbore contact friction is more severe, and the gravitational and hydrodynamic effects of the drilling fluid are more pronounced. Traditional added mass and damping methods struggle to fully capture the complex coupled dynamic behavior. This is a gap that [PERSON] et al. 's LBM-FEM approach aims to address by directly simulating the fluid dynamics and their interaction with the structure [44]. In view of this, the present study focuses on establishing effective numerical models to describe the dynamics of small-diameter horizontal drill strings and the two-way fluid-structure coupling effect. A recursive algorithm is employed for transient dynamics analysis, combined with the advanced Moving Particle Semi-implicit (MPS) method, to analyze the vibration response, frictional energy consumption, and flow field characteristics, thereby providing theoretical support and optimization guidance for the safe and efficient drilling of small-diameter horizontal wells.