Askat Kudaibergenov

The objective of this work is to apply machine learning algorithms for the analysis of dynamic vibrations of drill strings. As part of the research, a mathematical model describing the vibrations of the drill string was developed; a finite difference scheme was implemented, and numerical modeling was carried out using the three-point sweep method. Based on the data obtained from the numerical solution, a machine learning model was created. The numerical modeling was implemented using C++, while data collection and the construction of the machine learning model were performed using the Python programming language. As a result, a predictive model was obtained, capable of accurately forecasting the dynamic vibrations of the drill string and determining optimal parameters, thereby improving the efficiency and safety of drilling operations.

In this work, a software module for calculating drill string displacements taking into account the effect of a drilling fluid flow, external loads and the intermittent contact of the drill string with the borehole wall is developed. A generalized nonlinear mathematical model of the drill string spatial lateral vibrations underlies the module. The V.V. Novozhilov nonlinear elasticity theory and the Ostrogradsky-Hamilton variation principle were used to derive the mathematical model. To create the software module, the universal Wolfram Language with integrated computational intelligence is utilized. The functions for performing 2D visualization of the drill string spatial displacements, constructing phase portraits of the solution and conducting the comparative analysis of the obtained numerical results are included into the module. The developed module allows predicting the dynamics of the drill string before the beginning of well drilling due to the possibility of pre-setting the parameters of the drilling system and accounting for the environmental factors in the process of modeling for ensuring quick, safe and efficient exploration and production of natural resources.

In this paper, nonlinear vibrations of an infinite thin cylindrical shell as a limiting case of a nanotube are studied. The main relations of Sanders-Koiter’s nonlinear shell theory and the Hamilton variation principle are applied to obtain a nonlinear mathematical model of the shell vibrations and allow fully accounting for the influence of nonlinear effects. Using the method of multiple scales with specification of fast and slow times, high-order asymptotic relations taking into account quadratic and cubic nonlinearities are found. Based on the solution of the asymptotic scheme at fourth order and application of the inextensibility condition for the semi-membrane shell theory, the numerical analysis of tangential and radial displacements of the cylindrical shell at leading order relative to the Fourier coefficients is conducted. The impact of the wave number, polar angle, radius, and wall thickness of the shell on the amplitude and period of the arising vibrations is investigated. Numerical illustrations of the obtained solutions are presented for several cases.

In the first part of our review paper, we consider the problem of approximating the Green’s function of the Lagrange chain by continuous analogs. It is shown that the use of continuous equations based on the two-point Padé approximants gives good results. In the second part of the paper, the problem of singularities arising in the classical theory of elasticity with affecting concentrated loadings is considered. To overcome this problem, instead of a transition to the gradient theory of elasticity, it is proposed to change the concept of concentrated effort. Namely, the Dirac delta function is replaced by the Whittaker–Shannon–Kotel’nikov interpolating function. The only additional parameter that characterizes the microheterogeneity of the medium is used. An analog of the Flamant problem is considered as an example. The found solution does not contain singularities and tends to the classical one when the microheterogeneity parameter approaches zero. The derived formulas have a simpler form compared to those obtained by the gradient theory of elasticity.

This paper studies the stress-strain state of a rotating drill string complicated by the effect of a drilling mud flow and external compressive and twisting forces. The drill string is considered in the form of a homogeneous isotropic elastic rod with constant cross-section. A nonlinear mathematical model of the drill string spatial lateral vibrations based on Novozhilov’s nonlinear theory of elasticity is utilized. The Bubnov-Galerkin approach that allows reducing the given PDEs to ODEs and the numerical stiffness-switching method are applied to obtain a solution of the model. To analyze the stress-strain state of the drill string, we use the maximum stress intensity criterion and construct the graphs demonstrating changes of strain and stress in the chosen drill string cross-section with time, and stress distribution over the drill string length with time for nonlinear and linear cases. The research results indicate the significance of accounting for geometric nonlinearity to examine the drill string stress-strain state under the influence of the drilling mud.