Abstract
The paper investigates the nonlinear torsional dynamics of drill strings using mathematical and computational modeling. The study is motivated by the need to improve the reliability and efficiency of drilling processes under conditions when torsional vibrations affect the performance and the safety of drilling systems. A nonlinear mathematical model of the drill string is developed by treating it as a deformable rod with distributed parameters. The governing equations are derived from the Hamilton-Ostrogradsky variational principle under the assumption of finite strains within the framework of nonlinear elasticity. The distributed-parameter problem is reduced to a finite-dimensional system by means of the Bubnov-Galerkin method. Numerical simulations are performed to analyze the dynamic response of the considered systems and to evaluate the influence of geometric, dynamic, and physical parameters on drill string vibrations. The results show the effect of drill string length, angular velocity of the drill string, and material properties on the amplitude, frequency characteristics, modal interaction, and phase-plane structure of the nonlinear torsional response.