Reliable operation of intelligent rotary steerable systems (RSSs) critically depends on the dynamic stability of the bottom-hole assembly (BHA), where high-frequency vibrations can lead to tool malfunction, accelerating structural fatigue, and degrade steering performance under harsh downhole conditions. This study establishes a three-dimensional nonlinear coupled vibration model for a static push-the-bit RSS–BHA based on finite-element dynamics, energy-based methods, and Hamilton’s principle, enabling a unified analysis of axial, lateral, and torsional vibrations and their coupled responses under field-relevant high-frequency conditions. The results show that the proposed model can identify seven representative vibration modes commonly observed in drilling operations, including single-mode vibrations, pairwise coupled vibrations, and fully coupled vibration behaviors, and its predictive capability is validated through field-based case studies. Distinct dynamic characteristics clearly differentiate torsion-dominated stick–slip vibration from lateral–torsional coupled whirl vibration. Sensitivity analyses further demonstrate that stick–slip vibration is primarily governed by torsional excitation, whereas whirl vibration is dominated by lateral–torsional coupling and exhibits strong sensitivity to rotational speed and drill-collar geometry. Overall, this work provides a quantitative, physics-based framework for vibration-mode identification, interpretation of coupling mechanisms, and mode-specific vibration control and parameter optimization of RSS–BHA systems.
Shao et al. (Sat,) studied this question.