Modeling of Nonlinear Dynamics of Drill Strings in a Supersonic Air Flow

In this work we study nonlinear lateral vibrations of a drill string moving in a supersonic air flow. A nonlinear mathematical model of drill string vibrations is created on the basis of the nonlinear theory of elasticity making use of the Hamilton principle. Solution to the model is obtained by the Bubnov-Galerkin method in the first, second and third approximations. After reducing to a system of ordinary differential equations the numerical stiffness switching method is applied since the problem appears to be stiff. Comparative analysis of the nonlinear model and its geometrically linear analogue is carried out, and the significance of application of the governing equations taking into account geometric nonlinearity is shown. Drill strings with various parameters of length, operating frequency, axial force, and air flow pressure are investigated.