Abstract
In this article, the development and subsequent numerical analysis of a nonlinear mathematical model of the drill-string dynamics taking into account the effect of a drilling fluid flow and the gravitational energy of the system is carried out. Spatial lateral vibrations of the drill string modeled as a rotating elastic rod are studied. The developed nonlinear model generalizes and refines the well-known linear models of rod vibrations with the considered effect. The obtained numerical results demonstrate the influence of geometric nonlinearity, the gravitational energy of the drilling system, additional Coriolis and centrifugal forces as well as the parameters of the fluid flow on spatial vibrations of the drill strings. It allows for giving some recommendations on the choice of the drilling system parameters for ensuring safe drilling operations.