Abstract
In this work, we investigate the nonlinear dynamics of drilling equipment under operational conditions. The dynamic stability of a rotating drill string, accounting for prestress and finite deformations, is considered. Nonlinear vibrations associated with the spatial bending of the drill string are analyzed. Using the Bubnov–Galerkin and harmonic balance methods, the analysis of resonance regimes for both fundamental and higher-order harmonics is performed. Based on the Routh–Hurwitz criterion, instability zones for the third harmonic are identified. The numerical analysis demonstrates that the nonlinear interaction between harmonics generates a complex structure of vibrational regimes and directly influences the stability of the system.