(untitled) (International Journal of Mathematics and Physics, 2015)
Nonlinear flexural-torsional vibrations of shallow drill-strings are investigated. The drill-string is represented as an elastic rod rotating at constant angular velocity under the action of the longitudinal compressive force. The nonlinear model of flexural and torsional vibrations of drill-string is constructed on the basis of the theory of finite deformations of V.V. Novozhilov and its second system of simplifications. The numerical analysis of the model is carried out in the environment of symbolic mathematical computations - Wolfram Mathematica. The dominance of flexural vibrations of the drill-string over torsional vibrations is established. The influence of drill-string parameters on its oscillatory processes is investigated. It will allow to build up the modes of the drill-string movements to improve the quality of drilling of wells.