To address whirling- and vibration-induced failures in ultra-deep well drill strings caused by high slenderness ratios and complex loading conditions, this study establishes a nonlinear dynamic finite element model for a steel–titanium alloy composite drill string. The model is discretized with Euler–Bernoulli beam elements and solved using Newmark time integration combined with an iterative node-based spatial solution. Weight on bit, torque, wellbore–wall friction, impact/contact force, and equivalent drilling-fluid damping are considered. The model is used to evaluate how titanium alloy section size, length, wall thickness, and installation position affect whirling, lateral vibration, and torsional vibration. The results show that increasing drill-string diameter reduces the whirling range and lateral vibration intensity; when the diameter exceeds 149.23 mm, wall-impact frequency decreases markedly. Although the titanium alloy section exhibits approximately 60% higher local lateral vibration intensity than the steel section, the upper steel section experiences an approximately 18% reduction in lateral vibration. Installing the titanium alloy section in the middle of the string rather than near the bit reduces the overall lateral vibration intensity by approximately 30% and torsional vibration intensity by approximately 40%. Based on comparative sensitivity analysis, a titanium alloy section length of 1000–2000 m, diameter not less than 139.7 mm, and wall thickness not less than 12.7 mm are recommended for the simulated ultra-deep well conditions. These findings provide quantitative guidance for safer and more stable composite drill-string design.

This study investigates the influence of rotary speed on drill string whirl and vibration in 10,000 m ultra-deep wells through dynamic similarity experiments. A 1:4 geometrically scaled drill string–wellbore model was tested at 50–400 rpm under a weight on bit of 0.7 t and a torque of 100 N·m. Three laser rangefinders were used to reconstruct the drill string center trajectory and determine its translational and orbital responses. Forward whirl occurred at 50 and 100 rpm, a transition in whirl direction emerged at 350 rpm, and sustained backward whirl developed at 400 rpm, identifying 350–400 rpm as the critical transition interval. After zero-phase Butterworth filtering, the maximum center velocity increased from 0.241 to 0.579 m/s, while the maximum center acceleration rose from 3.014 to 15.813 m/s² and approached a plateau. The signed orbital angular velocity reversed from approximately +2975 rpm at low speeds to −2857 rpm at 400 rpm, whereas orbital angular acceleration exhibited a non-monotonic response. The measured vibration acceleration at 100 rpm was comparable in magnitude to field data from well SHY001-X3, supporting the physical plausibility of the observed trends. These results demonstrate that drill string vibration risk should be evaluated using multiple dynamic indicators. The experiments support qualitative identification of whirl transition and vibration risk intervals, although quantitative field prediction requires coupled models that account for fluid effects, structural dynamics, and contact interactions, together with calibration against full-scale measurements.