Free vibrations of drill strings in hyper deep vertical bore-wells

This paper considers the problems on investigation of the dynamic bending of elongated drill string tubes studied with allowance made for destabilizing effects of the longitudinal non-uniform preloading, action of torque, inertia forces of rotation and internal flows of washing liquid (mud). As a result of the completed analysis, natural wave and vibration modes are constructed, their frequencies are calculated. It is shown through the study of appropriate dispersion equations that free bending vibrations of unbounded rods can be realized only in the modes of regular dextral and sinistral spiral waves propagating with different velocities in different directions. The modes of free vibrations of the bounded drill strings possess more complicated irregular spiral shapes.