@article{Kudaibergenov_Khajiyeva_2018, title={On dynamic stability of drill strings in a supersonic gas flow}, volume={97}, url={https://bm.kaznu.kz/index.php/kaznu/article/view/488}, DOI={10.26577/jmmcs-2018-1-488}, abstractNote={<p>In this work stability of the drill string nonlinear dynamics, complicated by the effect of an external<br>axial load, initial curvature of the drill string, geometric nonlinearity and the influence of a<br>supersonic gas flow as a circulating medium is studied. The drill string is modelled as a rotating<br>elastic isotropic rod with constant cross-section. Pressure of the gas flow used to clean the borehole<br>from drill cuttings and to transport them from the bottom to the surface is determined by the<br>nonlinear dependences of the piston theory in the third approximation. Utilization of the Galerkin<br>method allows to reduce the drill string mathematical model to an ordinary differential equation<br>for the generalized time function, containing an asymmetric nonlinear characteristic, which is further<br>eliminated by introducing the corresponding substitution. Considering a small perturbation<br>to the system and applying the harmonic balance method, characteristic determinants are constructed.<br>Equations describing boundaries of instability zones of basic resonance, which allow to<br>determine the range of dangerous frequency regimes and to increase safety of the drilling process,<br>are obtained.</p>}, number={1}, journal={Journal of Mathematics, Mechanics and Computer Science}, author={Kudaibergenov, Askat K. and Khajiyeva, L. A.}, year={2018}, month={Aug.}, pages={101–110} }