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The problem of the self-excitation of the torsional oscillations of a drillstring rotating in a fluid in a deep borehole is stated. Three models describing the mechanical interaction between the drillstring and the viscous fluid are discussed. Governing equations with ordinary and partial derivatives are derived. A method to solve them is developed. Computer simulation shows that the self-oscillations are relaxational and the curves of the functions that describe them have sections of fast and slow motions. The results of simulation can be used to develop a technique for drilling deep oil and gas boreholes

The whirling vibrations of a rotating drillstring bottom-hole assembly subject to the moment of friction are analyzed qualitatively. A problem statement and solution are given. The self-excitation of vibrations is simulated. It is established that during the self-excitation of whirling vibrations, the axial line of the drill bit can slowly and rapidly move over intricately shaped nonsmooth conical surfaces

The propagation and evolution of the fronts of discontinuous waves in inhomogeneous transversely isotropic elastic media are studied. A method to draw evolving rays and fronts is proposed. Geometrical singularities on the fronts are studied for different parameters of anisotropy and inhomogeneity

The problem of elastic bending of drillstrings in deep curved boreholes with geometrically imperfect axial lines is stated based on the theory of curved flexible bars. The dependence of the force resisting the motion of the drillstring on the amplitude, spacing, and location of geometric imperfections is analyzed numerically. The numerical results are discussed

A wave model of torsional vibrations of rotating drill strings is set up. The ranges of rotational speed in which self-excited vibrations occur are found. Andronov–Hopf bifurcations occur at the limits of these ranges. The conditions for the occurrence and development of self-excited oscillatory processes are established

The paper deals with problem of critical states in single-support rods and cylindrical shells under axial follower forces and centrifugal inertial forces due to rotation. It is shown that depending on the relationship between these forces, loss of stability may be quasistatic or dynamic

A mathematical model is proposed to describe the critical quasistatic equilibrium of rotating drillstrings with additional centralizers in the lower portion. It is shown that the system of differential equations describing them is stiff. It is solved by decomposition. Drillstrings of different lengths are considered, the critical angular velocities are found, and buckling modes are identified

The ray method is used to develop a procedure for studying the kinematics and dynamics of the interaction of discontinuous waves with interfaces between elastic media. The critical states of such interactions are analyzed. For the cases of a free surface and two surfaces contacting with and without sliding, it is established that the kinematic and dynamic conditions for critical states to occur are satisfied simultaneously

The problem of propagation of bending waves in rotating pipes prestressed by longitudinal force and torque is stated and solved. Such waves are shown to be spiral ones. It is established that four waves exist for every wavelength, two of which are right-handed spirals and the other two are left-handed. These waves propagate with different velocities in different directions

The equations of balance of external and internal forces acting on a drillstring in a curved well are set up based on the formulations of direct and inverse problems in the mechanics of flexible curvilinear rods. The lowering, lifting, and rotation of a drillstring are studied. A method is proposed to calculate the internal longitudinal force, the forces of interaction between the drillstring and the well wall, and the forces of friction. An example is considered. It is shown that even small geometrical imperfections of the well path have a significant effect on the balance of external and internal forces

A mathematical model is proposed to describe the critical quasistatic equilibrium of long rotating drillstrings. The prestress of drillstrings by the gravity and torsion forces, the gyroscopic interaction of rotary and linear motions, and the destabilizing effect of the internal flow of the drilling fluid are taken into account. The phenomena accompanying the drilling to different depths are studied numerically

The quasistatic stability of a rotating drillstring under longitudinal force and torque is analyzed. Constitutive equations are derived, and a technique to solve them is proposed. It is shown that the buckling mode of the drillstring is helical within a section subjected to compressive forces

The influence of the curving and twisting of an elongated blade on its vibrations during complex rotation is studied. It is shown that these geometrical factors may cause additional resonant vibrations

A structural analysis of a large orbital antenna is reduced to stress–strain, stability, and modal analyses of its prestressed structure. The numerical results obtained by the finite-element method are presented

Steady precession vibrations of a single-support thin-walled rotor whose rotation axis is forced to make an additional rotation are simulated numerically. It is established that compared with double-support rotors, single-support rotors are more dynamically compliant and undergo two precession resonances over the range of rotation speeds being considered. Mode shapes of precession vibrations are drawn

The interaction of a plane discontinuous wave with the free curvilinear surface of an anisotropic elastic medium is studied. The ray-path method is used to describe the wavefront. The nonlinear Snell's equations are solved by combining Newton's method and the parameter continuation algorithm. The cases of focusing and scattering of wave rays are studied

This paper addresses issues of the theoretical dynamic analysis of elastic links making large relative translational and rotational motions. Mathematical models and analysis techniques for elastic vibrations of such systems are described. Examples of applied problems are adduced

Equations for studying the axisymmetric deformation of a cylindrical shell are derived on the basis of Timoshenko shell theory. A dispersion equation is set up to study natural harmonic waves in a cylindrical isotropic shell. A numerical approach to plotting dispersion diagrams is proposed. The wave velocities obtained coincide with analytical solutions

Kinematic and dynamic control problems for a pedestal-mounted robot with a multilink arm are formulated. The robot is considered a system of perfectly rigid bodies controlled by a combined actuating system. The mathematical model of robot dynamics accounts for the elastic properties of actuator components based on the formalism of Lagrange equations of the second kind. The effect of the elastic compliance of the actuator components on the dynamics of manipulator links and actuator motors is discussed. A robot with a two-link arm is considered as an example

Consideration is given to bifurcation problems for thin-walled spherical shells in simple and compound rotation. Similarities and differences in the formulations of such problems and techniques for their solution are pointed out. In both cases, the buckling mode is described by the first circumferential harmonic. An analysis is made of how the bifurcations of a shell depend on its geometry.

The problems of dynamic and kinematic control of a multilink robot manipulator are formulated. The distributed elasticity and inertia of the manipulator links are taken into account on the basis of the Timoshenko-beam model on the assumption that each of its elements moves complexly. The results obtained here are compared with data on the dynamic characteristics of a manipulator with rigid links and a manipulator with elastic links, whose elastic properties were simulated on the basis of the Euler–Bernoulli-beam model

The precession vibrations of a thin spherical segment during complex rotation are studied. These vibrations are simulated theoretically and experimentally. The results obtained for various diameters of the fixed circular contour are compared

The problem on the motion of concentrated forces over a beam on an elastic base is solved on the basis of the Timoshenko beam theory. Motion modes are constructed and three critical values of the velocity are found. The solution obtained is compared with that for the Kirchhoff beam

A study is made of the problem of precessional vibrations excited in a thin-walled rotor with a branching meridional section by gyroscopic inertial forces during the complex rotation of the rotor. Methods of solving the problem are proposed. It is established that resonant vibrations may be excited while the rotor is undergoing complex rotation.

A problem of diffraction of an incident-wave front interacting with an interface is considered within the framework of shock-wave theory for anisotropic elastic media. An approach to geometrical construction of reflected- and refracted-wave fronts using methods of continuation by a parameter is proposed for solution of Snellius generalized nonlinear equations. A numerical example is presented.

Analysis of the results indicates that: a) all the optimal trajectories may be divided into two sections: the phased section, corresponding to motion over a trajectory close to the initial one with a small change in initial energy (amounting to around two-thirds of the total journey time); and the orbital transfer, with considerable change in orbital energy, as a result of active control of the solar-sail orientation (around one-third of the total journey time). In the second section, the spacecraft first moves closer to the Sun and then makes the transfer to Mars orbit; b) the duration of orbital transfer is 581 dyas according to the optimal plan, which includes sections of deceleration and movement from the initial orbit over a distance of 0.2 dimensional length units toward the Sun; with the constraint ϑ

A basic component of modern thermal and atomic power stations is curvilinear heat-exchanger tubing containing pulsed internal fluxes caused by inhomogeneous masses of boiling liquid, vapor, and their mixture. To increase the efficiency of heat transfer, tubes have been constructed as cylindrical helical coils which develops centrifugal inertial forces which are proportional to the curvature, the mass of the moving fluid and the square of its velocity. In the present work, the influence of the size of the breakaway liquid portions and their velocity on the dynamic behavior of a cylindrical helical tube is investigated. The equations of curvilinear-rod flexure, intensity vectors of the inertial force, and the curvature/torsional parameters of the helix are discussed.

The dynamics of transient process during a controlled change in the mutual orientation of the axis of the flexible disk and carrying body is investigated