bluuebunny/crossref_metadata_2025 huggingface dataset:
Effective Tensor of the Relaxation Kernels of a Layered Medium Consisting of a Viscoelastic Material and a Viscous Incompressible Fluid
Authors: Shumilova V. V.
Published: April 2024

The explicit formulas for calculating the components of the effective tensor of relaxation kernels of a two-phase layered medium with a periodic microstructure are derived. The first phase of such a medium consists of an isotropic viscoelastic material and the second phase consists of a viscous incompressible fluid. In particular, it is established that the components of this tensor depend on the volume fraction of the fluid inside a periodicity cell and do not depend on the number of layers and the distances between them.
Effect of Confinement of Flow by Side Walls on the Cross Flow
Authors: Dushina O. A. , Kalinin E. I. , Klyuev M. A. , Mazo A. B. , Molochnikov V. M.
Published: April 2024

The effect of confinement of flow over the transversal coordinate on cross flow past a circular cylinder at the Reynolds numbers from 40 to 255 (based on the cylinder diameter and the undisturbed flow velocity) is studied numerically and experimentally. In the experiments, the cylinder was located in a rectangular channel and, in the case of numerical simulation, three types of the boundary conditions, namely, the periodic boundary conditions and the slip and no-slip conditions were imposed on the side walls confining the flow. Particular attention is concentrated on the vertical flow structure in the cylinder wake. It is shown that spiral vortices that travel in the plane of symmetry of the channel are formed only in the case of no-slip boundary conditions in the region of junction of the cylinder and the side walls. Under their interaction, vortex clusters are formed in the center of channel and some indications to flow turbulization can be observed in the wake. Under the periodic boundary conditions and the slip conditions on the side walls, there are no spiral vortices and, in the Re range from 200 to 250, the A and B modes of three-dimensional instability and turbulence transition are implemented in the cylinder wake. The effect of the channel width and the type of boundary conditions on the side walls on the vortex wake structure behind the cylinder and integral flow parameters is estimated.
Flow past Rankine’s Half-Body of Revolution
Authors: Korolev G. L. , Sychev Vik. V.
Published: April 2024

An axisymmetric incompressible flow past Rankine’s half-body of revolution is investigated at high Reynolds numbers. It is established that the solution of the problem for the system of boundary layer equations does not involve the line of zero surface friction. The low under consideration is separationless, which is in complete agreement with the available experimental data.
Duality of the stream pattern of supersonic viscous gas flow past a blunt-fin junction: effect of a low sweep angle
Authors: KOLESNIK E. V. , SMIRNOV E. M.
Published: April 2024

Results of numerical solution of the problem of supersonic flow past a symmetric blunt fin mounted on a plate with a developing boundary layer are presented. Generally, the case considered corresponds to the flow configuration used in the experimental and computational study by Tutty et al. (2013), in which the laminar air flow with the freestream Mach number of 6.7 is considered. Previously, the authors have shown (2020) that for these conditions two stable solutions corresponding to metastable flow states with different configurations of the vortex structure and the pattern of local heat transfer are predicted. In present paper, the influence of a low sweep angle of a blunt leading edge on the vortex structure in the separation region, local heat transfer, and the possibility of obtaining a dual solution are investigated. The bifurcation diagrams showing for two solutions the main horseshoe vortex center location and the length of separation region versus the skew angle are presented.
Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient
Catastrophe
Authors: Aksenov A. V. , Druzhkov K. P.
Published: April 2024

The system of equations that describes one-dimensional polytropic gas flows is considered. The invariants up to the second order of characteristics of the considered system of equations are classified. The method of reducing the Cauchy problems to systems of ordinary differential equations is proposed. Examples of the solutions without gradient catastrophe are constructed using invariants of characteristics supplementary to the Riemann invariants.
Comparison of the Eulerian and Lagrangian Approaches to Studying the Peculiarities of the Interstellar Dust Distribution in the Heliosphere in the Framework of the Cold Gas Model
Authors: Godenko E. A. , Izmodenov V. V.
Published: April 2024

Interstellar dust grains penetrate into the heliosphere (region in which the solar wind propagates) due to the relative motion of the Sun and the Local Interstellar Medium (LISM). Inside the heliosphere, the motion of dust particles is mainly governed by the electromagnetic force determined by the heliospheric magnetic field. Under the action of this force, the trajectories of dust grains experience intersections with each other and self-intersections. As a result, dust density accumulation regions appear. These regions are of a great interest in the context of theoretical studying and planning of upcoming space missions. The main aim of the present study is to model the interstellar dust distribution in the heliosphere and investigate the peculiarities of the number density distribution. To describe the dusty component, the cold gas model is used, while to compute the interstellar dust distribution two approaches are considered, namely, the Eulerian and Lagrangian approaches. For solving the continuity equation in the Lagrangian coordinates, the full Lagrangian method or the Osiptsov method is used. As a result, all the peculiarities of the dust distribution are investigated and it is found that they are located on caustics, i.e., the envelopes of interstellar dust trajectories. Besides it, the regular regions of overdensity (without singularities in the number density) are discovered. It is shown that the dust component accumulation regions are located in a small neighborhood of the heliospheric current sheet, at which the magnetic field changes its polarity, and in the tail of the heliosphere. The effectiveness of the Osiptsov method of solving the continuity equation is compared with the widely used Monte Carlo method (Eulerian approach). It is shown that Monte Carlo method requires extremely high resolution of computational grid to reach the level of accuracy comparable with the Osiptsov method.
Reconstruction of Three-Dimensional Structures of Electrohydrodynamic Flows Induced by Blade-Plane Geometry
Authors: Yan Z. , Louste C. , Fang J. , Wu W.
Published: April 2024

Particle image velocimetry (PIV) method has emerged as a powerful technique for electrohydrodynamic (EHD) flow field measurements. Based on a series of parallel field measurements along the blade electrode, we reconstruct the three-dimensional (3D) structure of EHD flows produced by an actuator in the blade-plane geometry. A non-uniform distribution of injection intensity and velocity is observed along the electrode. With the aid of slice plots from different views of 3D Cartesian, it is understood that the applied voltage, electrode spacing and the electrode surface or tip roughness exert a remarkable effect upon the structure of EHD jets. The findings of this investigation will complement the full view of the 3D structure of the jet and be of broad use to guide the selection of appropriate positions along the blade for profile plane studies.
Pulsating Turbulent Flows through a Square Pipe
Authors: Nikitin N. V. , Popelenskaya N. V.
Published: April 2024

Pulsating turbulent flows in a square pipe are studied numerically. The flow dominance regime in which the fluid flow rate remains positive in all phases of the oscillatory cycle is considered. The flows are studied at several oscillation frequencies. The results are compared with oscillating laminar flows and a steady turbulent flow in a square pipe, as well as with pulsating turbulent flows in a round pipe. The integral and fluctuating characteristics of turbulence and their dependence on the oscillation frequency are determined. In particular, it is found that at the considered Reynolds number Re = 2200 the friction coefficient in pulsating flows turns out to be lower than that in the stationary flows. The drag reduction increases with growth of the oscillation period and reaches 14.7%. A distinctive feature of turbulent flows in pipes of rectangular cross-section is the occurrence of secondary flows of Prandtl’s 2nd kind. The details of secondary flows under the pulsating flow conditions are studied at length.
Hydromechanical Modeling of the Deep Initial Impulsive Action on the Hydrogeophysical Massif
Authors: Anakhaev K. N. , Belikov V. V.
Published: April 2024

The article considers the potential problem of a deep impulsive impact at the initial moment of time on a hydrogeophysical massif, which can occur during underground (underwater) explosions, volcanic eruptions, seismic events, etc. The impact of the pulse focus was modeled by a rounded source with a unit pressure, and the sink area was modeled by a line of zero potential. A rigorous hydromechanical solution of the problem is obtained with the establishment of an analytical relationship between the physical region of the flow and the complex potential based on the theory of the function of a complex variable, that is, the use of the method of successive conformal mappings with the determination of all necessary flow characteristics. Calculation examples are given for special cases with the construction of curvilinear orthogonal hydrodynamic grids, outlines of families of lines of equal heads and stream lines, profiles of impulse sources, as well as diagrams of velocities, heads and potential flow rates.
Solution of the External Pochhammer-Chree Problem and Bending Seismic Vibrations of the Pipeline in Infinite Elastic Continuu
Authors: Israilov M. Sh.
Published: April 2024

The possibility of partial splitting of the dynamic equations of the linear theory of elasticity for bulk expansion and the components of the rotation vector of medium particles in cylindrical coordinates in the general case of a nonstationary problem is proved. This result is a generalization of a similar fact established by A. Love with a simple harmonic dependence of the named functions on time and two spatial coordinates. An exact analytical solution of the problem on bending vibrations of an elastic space with a circular cylindrical cavity (external Pochhammer-Chree problem) is given. It is shown that the study published by K. Toki and Sh. Takada on this problem does not provide a solution to the posed problem. On the basis of the solution obtained for the external Pochhammer-Chree problem, bending vibrations of an underground pipeline caused by the action of a seismic wave are studied. The results obtained in this case provide, apparently, the first theoretical substantiation of the engineering theory of rigid jamming of the pipeline in the soil for the case of bending vibrations, widely used in regulatory documents on seismic construction.
Optimal Acceleration or Braking of Massive Flywheels at the Strength Limit
Authors: Brigadnov I. A. , Maksarov V. V. , Olt J C
Published: April 2024

The article poses and solves the problem on time-optimal control of the quasi-static acceleration or deceleration of a massive flywheel by taking into account the strength properties of the material. The dependence of optimal regimes on parameters is investigated and features of optimal regimes are revealed. For disk and long cylindrical flywheels, universal optimal modes of acceleration or deceleration that can be used in the design or operation of inertial energy storage devices are built.
On the Dynamics of Some Systems with Impacts and One-Way Constraints
Authors: Rosenblat H. M. , Borisov S. V.
Published: April 2024

The article considers some problems of mechanics about the rolling of a wheel with impacts and one-way constraints under dry friction. Such tasks are often encountered in practice when a vehicle wheel collides with or leaves an obstacle. The contact of the wheel with the road is assumed to be point, the dry friction model is the classical Euler-Coulomb model. A complete analysis of various cases of impact and post-impact movements of the wheel is given.
Application of Methods of the Theory of Critical Distances to Estimate the Fracture of Quasi-Brittle Materials with Notches
Authors: Suknev S. V.
Published: April 2024

The application of various methods of the theory of critical distances for evaluating the cleavage failure of a quasi-brittle plate with a notch in the form of a circular hole that is subjected to uniaxial tension, uniaxial compression, and also to the combined action of tensile and compressive stresses is considered. Critical stress calculations have been performed based on the previously proposed approach, according to which the structural parameter of the nonlocal failure criterion is represented as the sum of two terms. The first of them characterizes the actual structure of the material and is a constant, while the second one reflects the formation of inelastic deformations and depends on the plastic properties of the material, sample geometry, and boundary conditions. The calculation results are compared with known experimental data.
On the Relative Equilibria of a Heavy Bead on a Uniformly Rotating Rough Spoke
Authors: Burov A. A. , Nikonov V. I.
Published: April 2024

The movement of a heavy bead strung on a rough spoke, uniformly rotating around a vertical axis, is considered. Under the assumption that the spoke and the axis of rotation are crossed, the existence of sets of non-isolated relative equilibria of the bead and their dependence on parameters are studied. The problem is a natural generalization of the well-known Sommerfeld problem, which assumes that the spoke and the axis of rotation intersect.
Viscoplastic Flow in the Material of a Cylindrical Layer Suspended on a Rigid Shaft under the Conditions of Its Variable Rotation
Authors: Firsov S. V.
Published: April 2024

The development of viscoplastic flow in the material of a cylindrical layer placed on a rigid cylindrical shaft and rotating with it around their common axis is calculated. Depending on the increasing speed of rotation up to the maximum, the place and time points of the beginning of the viscoplastic flow, the patterns of propagation of the flow area, the changing strains and stresses in the deformable material are determined. As a condition for viscoplastic flow, the corresponding generalization of the condition for maximum octahedral stresses is taken. For the purposes of testing the calculation programs, an exact solution of the problem of a steady viscoplastic flow of a material during rotation of a compound cylinder at a constant speed has been obtained.
Peculiarities of Body Balance on Hinged Supports and Sliding Closure
Authors: Dosaev M. Z. , Samsonov V. A.
Published: April 2024

The equilibrium of a body supported by rigid and telescopic supports on fixed hinges is considered. It is shown that the addition of a potentially sliding joint may not provide mobility to the design, as well as the addition of a rotary joint. A paradox was discovered for a sliding support: the equations of seemingly obvious equilibrium are not fulfilled. Deviations are introduced to regularize the problem. Internal reactions remain statically indeterminate, while the magnitude of these reactions may be significant. It is shown that external reactions tend to infinity as the introduced deviations decrease. This explains the inconsistency of the equilibrium equations: a pair of infinite forces with zero leverage, generally speaking, is not equivalent to zero force, but can create any moment, including the balancing moment of gravity. It can be assumed that some of the major accidents involving building structures are associated with these features.
Solution of Problems of Elasticity Theory for Multiply Connected Half-Planes and Strips
Authors: Kaloerov S. A. , Glushankov E. S. , Mironenko A. B.
Published: April 2024

A general solution of problems of elasticity theory for anisotropic half-planes and strips with arbitrary holes and cracks is presented, which uses the complex potentials of the plane problem of the theory of elasticity of an anisotropic body, conformal mappings, representations of holomorphic functions by Laurent series, and satisfaction of boundary conditions by the generalized least squares method. The problems are reduced to overdetermined systems of linear algebraic equations solved by the singular value decomposition. The results of numerical studies are described for a strip with a circular hole under its tension or under the action of a uniform pressure along a segment of a rectilinear boundary, as well as for the tension of a strip with a circular hole and a crack in the bridge, including those extending to the border of the strip or to the contour of the hole. An isotropic half-plane and a strip with holes and cracks are considered as special cases of the general problem. The influence of the geometric characteristics of holes and cracks, the physical and mechanical properties of the strip on the values and distribution of stresses material was studied.
Relative Equilibria of a Heavy Point on a Uniformly Rotating Inclined Plane
Authors: Burov A. A. , Nikonov V. I.
Published: April 2024

The problem of the motion of a heavy point along an inclined plane that rotates uniformly around the vertical is considered. The area filled with non-isolated relative equilibria is determined, its dependence on the parameters of the problem - the angular velocity, the angle of inclination of the plane and the angle of friction - is studied. The stability of the studied relative equilibria is discussed.
The Problem of Boundary Control of Displacement at Two Ends by the Process of Oscillation of a Rod Consisting of Two Sections of Different Density and Elasticity
Authors: Barseghyan V. R.
Published: April 2024

The problem of boundary control for a one-dimensional wave equation with piecewise constant characteristics is considered. In this case, it is assumed that the time of passage of the wave through each homogeneous section is the same. The control is carried out by displacement at both ends. A constructive approach to constructing a control action with given initial and final conditions is proposed. The construction scheme is as follows: the original problem is reduced to the problem of controlling distributed influences with zero boundary conditions. Further, the method of separation of variables and methods of control theory for finite-dimensional systems are used. The results obtained are illustrated by a specific example.
Solution of the Dynamic Lame Problem
Authors: Rasulova N. B. , Mahmudzade T. M.
Published: April 2024

The well-known Lame problem, posed in 1852, involves solving the static equilibrium of a parallelepiped with free side surfaces subjected to action of opposite end forces. In this article, the same problem for a more complicated case of impacts of end forces is considered.
An exact analytical solution of this problem is found.
Emphasizing the particular difficulty of solving this problem, Lamé, in his book “Leçons sur la thorie mathematique de Ielasticite des corps solides” (Paris, 1852), wrote: “C’est une sorte d’engine aussi digne d’exercer la sagasite des analystes que le fameux problem des trios corps de la Mécanique celeste”,—“This is a kind of drive, as worthy of training the clairvoyance of analysts as the famous three-body problem of celestial mechanics.” At that time, this problem was the subject of a prize from the Paris Academy of Sciences, that was intended for the one who solved the Lamé problem. Despite this, to date, no solution has been found even for a static case of this problem, not to mention the complicated version of the problem.
Quaternion Methods and Regular Models of Celestial Mechanics and Space Flight Mechanics: Local Regularization of the Singularities of the Equations of the Perturbed Spatial Restricted Three-Body Problem Generated by Gravitational Forces
Authors: Chelnokov Yu. N.
Published: April 2024

The problem of local regularization of differential equations of a perturbed spatial restricted three-body problem is studied: elimination of singularities (dividing by zero) generated by gravity forces of differential equations of perturbed spatial motion of a material point M, which has a negligibly small mass, in the vicinity of two gravitating points M0 and M1 by writing equations of motion in rotating coordinate systems, the use of new regular variables and the regularizing transformation of time. Various systems of regular quaternion differential equations (RQDE) for this problem are obtained. The following groups of variables act as variables in these equations: (1) four-dimensional Kustaanheimo–Stiefel variables, Keplerian energies and time t, (2) distances from the point M to the points M0 and M1, modules of the vectors of the moment of velocities of the point M with respect to the points M0 and M1, Keplerian energy, time t and Euler (Rodrigues–Hamilton) parameters characterizing the orientations of the orbital coordinate systems in the inertial coordinate system; (3) two-dimensional Levi-Civita variables describing the motion of the point M in ideal coordinate systems, Keplerian energies, time t and Euler parameters characterizing the orientations of ideal coordinate systems in the inertial coordinate system and being osculating elements (slowly changing variables) for the motion of the point M in the neighborhood gravitating point M0 or M1, respectively. To construct the RQDE, the equations of the perturbed spatial restricted three-body problem, written either in nonholonomic (azimuthally free), or in orbital, or in ideal coordinate systems, were used as initial ones; “fictitious” times τ0 and τ1 are used as new independent variables (i.e., regularizing differential transformations of the Sundmann time are used) or angular variables φ0 and φ1, which are traditionally used in the study of orbital motion as part of polar coordinates. To match the two independent variables used in the vicinity of the gravitating points M0 and M1, additional differential equations are used.
The obtained various locally regular quaternion differential equations of the perturbed spatial restricted three-body problem make it possible to develop regular analytical and numerical methods for studying the motion of a body of negligibly small mass in the vicinity of two other bodies with finite masses, and also make it possible to construct regular algorithms for the numerical integration of these equations. The equations can be effectively used to study the orbital motion of celestial and cosmic bodies and spacecraft, to predict their motion, as well as to solve problems of controlling the orbital motion of spacecraft and solving problems of inertial navigation in space.
Asymptotic Study of Plate Bending for a Strongly Orthotropic Materia
Authors: Sheshenin S. V. , Muradkhanov R. R.
Published: April 2024

The technique of asymptotic averaging has been developed for three-dimensional partial differential equations with rapidly oscillating coefficients. For example, for the equations of elasticity theory. Then it was modified and applied to thin bodies in the form of plates (homogeneous or inhomogeneous, with even front surfaces or not), described by the three-dimensional theory of elasticity. In these cases, asymptotic solutions were constructed with respect to one small parameter, which is usually the ratio of the plate thickness to the characteristic plan size. The averaging technique in this case also reduces the dimension of the problem, i.e. reduces the three-dimensional boundary value problem to some two-dimensional one.
In this article, we substantiate the application of the method to a problem with two small parameters in the case of a homogeneous thin, highly orthotropic plate bent by a surface load without taking into account body forces. The second small parameter is the ratio of the transverse elastic moduli to the moduli in the plan of the plate. It is shown that strong orthotropy is equivalent to an increase in the thickness of the equivalent plate.
A procedure for obtaining the stress distribution over the plate thickness is described for three approximations. The first approximation gives the classical Kirchhoff theory, also called the Kirchhoff-Love theory, and the third approximation coincides with the Ambartsumian theory and allows one to find transverse shear and normal stresses. The consideration of cylindrical bending makes it possible to find solutions in the framework of classical plate theories in the form of formulas, as well as three approximations of the asymptotic theory, which simplifies comparison. Examples are considered when the averaged orthotropic moduli are taken for a single-layer fibrous composite.
Statement of the Problem of Precessions of a Solid with a Fixed Point in Three Homogeneous Force Fields. Precession-Isoconic Body Movements
Authors: Gorr G. V.
Published: April 2024

The article considers the formulation of the problem of the motion of a solid with a fixed point in a force field, which is a superposition of three homogeneous fields. A new solution of the equations of motion is obtained, which describes the precession-isoconic motion with respect to the vertical.
Wear Calculation for a Radial Plain Bearing under Randomly Changing Temperature and Load
Authors: Soldatenkov I. A.
Published: April 2024

A stochastic model of the wear process of a thin coating in a radial plain bearing that takes into account random changes in the bearing temperature and external load is described. The results of a numerical analysis of the process of bearing wear in relation to the conditions of operation in open space at near-Earth orbital stations are presented. The importance of taking into account random changes in temperature and external load for predicting bearing wear and, in particular, its durability is evaluated.
Analysis of Dynamics and Control During the Deployment of an Annular Tether Group of Spacecraft
Authors: Zabolotnov Yu. M. , Nazarova A. A. , Wang Changqing
Published: April 2024

The article considers a method for forming a rotating tether group of small spacecraft in the form of a regular polygon. To create an external torque acting on the entire system as a whole, low-thrust engines are used, and the directions of the reactive forces are unchanged in the coordinate systems associated with the spacecraft. The release of the cables is controlled by measuring their length and speed in accordance with the nominal program, which assumes that the mechanisms of the release of the cables work only for their braking. The nominal program is built according to a simplified model of the system's motion, built using the Lagrange equations. The feasibility of the deployment program is checked using a more complete model of the spatial motion of the system, written in a geocentric fixed coordinate system and taking into account the extensibility of the cables, the one-sidedness of the mechanical links corresponding to them, the operation of the control system, disturbances associated with the initial conditions of motion, etc. A more complete model of motion takes into account the motion of space vehicles relative to their centers of mass as solid bodies of finite dimensions, which leads to perturbations in the directions of action of reactive forces. Numerical examples are given of the deployment of ring tether groups of small spacecraft in the form of polygons with up to seven vertices, inclusive, under the action of disturbances.
Dynamic Axisymmetric Tension of a Thin Round Ideally Rigid-Plastic Layer
Authors: Tsvetkov I. M.
Published: April 2024

We consider the stress-strain state that occurs during dynamic tension of a homogeneous round layer of an incompressible ideally rigid-plastic material that obeys the Mises–Genka criterion. The upper and lower bases are stress-free, and the radial velocity is set on the lateral boundary. The possibility of thickening or thinning of the layer is taken into account, which simulates neck formation and further development of the neck. Two characteristic tension modes are revealed. First one is associated with a rather high rate of removal of the side boundary of the layer from the center, the second one is associated with acceleration. In the second case, we have carried out an analysis using the method of asymptotic integration, which makes it possible to approximately find the parameters of the stress-strain state.
A Dynamicly Consistent Model of Normal Reactions at Points of a Mobile Platform Contact with a Surface Taking Account of the Design of Mecanum Wheels and Multicomponent Friction
Authors: Saipulaev G. R. , Adamov B. I. , Kobrin A. I.
Published: April 2024

The article investigates the influence of the dependence of normal reactions on motion parameters on the dynamics of a mobile platform by taking into account the design of mecanum wheels and multicomponent friction. To describe the dependence of normal reactions on motion parameters, the theorems on the change in momentum and angular momentum written for the mecanum platform are used. The influence of normal reactions on the dynamics of the mecanum platform is estimated from the results of numerical simulation. The mecanum platform dynamics model takes into account the design of the mecanum wheels and multicomponent friction. The multicomponent friction model proposed by V.F. Zhuravlev that takes into account sliding and spinning is considered. Estimates of the maximum deviations of the normal reactions of the supports, due to the dynamics of the mecanum platform, from the values of the normal reactions calculated for the mobile platform at rest (equal to 16.7% for KUKA youBot robot) are given. Inequalities that limit the maximum values of the control moments, under which the contacting rollers of the mecanum wheels do not come off from the supporting surface are obtained. Based on the simulation results, it is shown that the normal responses are changed by 5–6% of the normal response value calculated in the case of the mecanum platform at rest, which corresponds to the obtained estimates. These changes in normal reactions can lead to a decrease in the accuracy of the movement of the mecanum platform obtained with program control.
Nanoindentation of AlGaN Films Formed on SiC/Si Substrates Grown by the Method of Coordinated Substitution of Atoms
Authors: Grashchenko A. S. , Kukushkin S. A. , Osipov A. V. , Sharofidinov Sh. Sh.
Published: April 2024

In this article, the mechanical and deformation characteristics of epitaxial films of AlGaN solid solutions formed on silicon substrates of crystallographic orientations (001), (011) and (111) with a silicon carbide (SiC/Si) buffer layer synthesized by the method of the coordinated substitution of atoms were studied using the nanoindentation method. The growth of AlGaN epitaxial layers were carried out both directly on the SiC/Si hybrid substrate and on the SiC/Si substrate additionally coated with an AlN buffer layer. The morphology and structure of the surface of the layers was studied by atomic force microscopy. The structural characteristics of hybrid AlGaN substrates and films grown with and without an aluminum nitride buffer layer were measured. An unambiguous relationship has been established between the mechanical properties (elasticity modulus and hardness) and the surface structure of AlGaN films. It has been found that the AlN buffer layer has a significant effect on the mechanical and deformation properties of AlGaN films at the initial moment of indentation, when the layer is predominantly elastically deformed. The roughness was determined and the surface morphology of the AlGaN films was characterized. For the first time, experimentally, using the nanoindentation method, the hardness parameters and the reduced modulus of elasticity of epitaxial AlGaN grown on hybrid SiC/Si and AlN/SiC/Si substrates were measured.
Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution
Authors: Alekseyeva L. A. , Alipova B. N.
Published: April 2024

Using the model of coupled thermoelasticity, the boundary value problems of the dynamics of a thermoelastic half-space are solved for plane deformation with periodic surface force and thermal effects associated with the desired boundary functions by linear algebraic relations. Green’s tensors are constructed for the stated boundary value problems, using their properties, analytical solutions of these problems are obtained. To solve them, we have used the method of incomplete separation of variables, the Fourier transform, and the properties of fundamental solutions. The presented algorithm solves the classical four boundary value problems of thermoelasticity, as well as non-classical ones with coupled thermal and force characteristics at the boundary of the half-plane.
Structural Optimization of a Longitudinally Moving Layered Web Based on a Multi-Criteria Approach
Authors: Banichuk N. V. , Ivanova S. Yu. , Afanas'ev V. S.
Published: April 2024

The longitudinal motion at a constant speed of a thin continuous elastic web through a system of roller bearings under the action of a given constant tension is considered. One span between adjacent supports is considered. The web is modeled by a thin layered plate hinged on two opposite edges, the remaining two sides of the plate are free. It is assumed that the plate in the process of longitudinal movement can perform small transverse vibrations. The layers of the plate from a given set of materials are arranged symmetrically to the middle surface and fit tightly to each other. The total thickness of all layers is given and is small compared to the span length and plate width. Analytical expressions are derived for the effective characteristics of the plate, as a result of which the initial composite structure can be considered as an isotropic homogeneous plate, for which the known equations for calculating the critical velocity are applied. Within the framework of multi-criteria Pareto optimization, using a numerical method of non-local optimization, the order of the layers and their thickness are determined in order to satisfy a number of selected criteria: the maximum critical divergence rate, the maximum flexural stiffness, and the minimum unit weight of the layered web. An example of the found optimal structure of the plate and the constructed Pareto front for a given set of defining parameters of the problem are given.
A Family of Oscillations Connecting Stable and Unstable Permanent Rotations of a Heavy Solid with a Fixed Point
Authors: Tkhai V. N.
Published: April 2024

The rotation of a heavy rigid body around a fixed point is investigated if the center of gravity belongs to the main plane of the ellipsoid of inertia. A reduction of the system of Euler–Poisson equations to a reversible conservative system with two degrees of freedom is given, and a bifurcation analysis of permanent rotations is carried out. Global families of periodic motions are found that connect stable and unstable permanent rotations of the same frequency. It is proved that non-degenerate symmetric periodic motion in a reversible mechanical system always continues to the global family.
Plane Problem of the Theory of Elasticity on the Identification of Nodal Points of a Quadrature Inclusion
Authors: Kaptsov A. V. , Shifrin E. I.
Published: April 2024

The problem of detection and identification of an elastic inclusion in an isotropic, linearly elastic plane is considered. It is assumed that constant stresses are set at infinity. It is also assumed that on some closed curve containing an inclusion inside, the acting forces and displacements are known quantities. For the case of quadrature domain occupied by the inclusion, a method for identifying its nodal points has been developed. The developed method is based on the application of the principle of reciprocity. Numerical examples are given.
Studying the Properties of Metamaterials with a Negative Poisson’s Ratio when Punched by a Rigid Impactor
Authors: Ivanova S. Yu. , Osipenko K. Yu. , Demin A. I. , Banichuk N. V. , Lisovenko D. S.
Published: April 2024

Some properties of metamaterials with a negative Poisson’s ratio (auxetics) have been studied experimentally when punched along the normal by a rigid spherical impactor. Samples of a metamaterial with a chiral structure (hexachirals honeycomb) are made of e-PLA plastic using a 3D printer. In experiments, a deviation of the direction of movement of the impactor after leaving the punched sample from the approach direction (normal to the side surface) is observed. The dependence of the impactor projection direction on the orientation of the elements of chiral symmetry of the samples is established. A FE model for calculating the penetration of a chiral structure has been developed. Numerical results are presented and their agreement with experimental data is noted.
Anisotropy of Residual Stress Energy in Two-Component Plate Crystal Structures
Authors: Lisovenko D. S. , Epishin A. I.
Published: April 2024

An analytical solution for residual stresses and their energy in an elastically anisotropic two-component plate structure, where the components have an identical type of elastic anisotropy, identical or proportional elastic constants and coinciding principal axes of elastic anisotropy is obtained. The obtained solution has been applied to analyze the anisotropy of the elastic energy of such crystalline structures as the raft structure γ/γ' of single-crystal nickel-base superalloys, multilayer erosion-resistant nanocoatings ZrN/CrN and single-layer coatings of various types. It has been shown that the factor of minimizing the elastic energy of residual stresses has a significant effect on the crystallographic orientation of the interface in multilayer structures and the direction of axis of the growth texture axis of coatings.
Principal Problems of Relativistic Mechanics of Solids
Authors: Vasiliev V. V. , Fedorov L. V.
Published: April 2024

The article deals with a discussion of fundamental problems arising in relativistic mechanics (general relativity) in relation to the determination of stresses generated by gravity in a deformable solid. Three such problems are considered. The first one is associated with the incompleteness of Einstein’s system of equations that includes six mutually independent equations with ten unknown coefficients of the metric tensor. The second one arises when determining the stresses in a solid generated by gravity. For a static problem, three equations of the law of conservation of theory (equilibrium equations) include six unknown stresses, which, unlike Newton’s theory, does not allow determining gravitational stresses. The third problem is related to the reduction of linearized Einstein equations to the equations of Newton’s gravitational theory. Such a reduction turns out to be possible only for empty space and is not valid for a solid body. The noted contradictions can be eliminated by limiting the scope of the theory to a special space, which is Euclidean with respect to spatial coordinates and Riemannian only with respect to time. The discussion is illustrated by a spherically symmetric problem that reduces to ordinary differential equations.
International Diamond School–2023
Authors: Klepikov I. V.
Published: April 2024

The article contains an overview of reports and master classes at the International Diamond School, which took place in February 20–25, 2023 in Bressanone, Italy. The School touched upon such aspects of the study of natural diamonds as geochemical and isotope features and morphology of crystals, composition of inclusions in them, geological conditions of formation, as well as interesting debatable issues.
Structural Transformations of Minerals in the Earth’s Mantle: the New High Pressure Polymorphous Modifications of Olivine and Wollastonite
Authors: Pushcharovsky D. Yu.
Published: April 2024

There are reviewed important results obtained in the studies of HP-minerals during 2018–2022 years. The emphasis is made on the characterization of HP-polymorphs modifications of olivine (asimovite, poirierite) and wollastonite (breyite and davemaoite) discovered in this period. The structure of poirierite (ε-Mg2SiO4) contains the unique silicate chain Si3O9 with one tetrahedron in its period. Consequently its structural formula is Mg2[SiO3]O, and its intergrowth with wadsleyite/ringwoodite in shocked chondrites support the idea that transformations of olivine into ringwoodite becomes via forming of poirierite. The close ratio of cell parameters in wollastonite (1T) at 8.9 GPa and its synthetic analogue CaGeO3 exhibits the similarity of their structures. The HP/HT data confirm the stability of the wollastonite polymorph (1T, 2M, pseudowollastonite and synthetic analogue of breyite) at the upper mantle conditions. The crystal structures and composition of new НР-minerals discovered as inclusions in diamonds, in meteorites and in the rocks near terrestrial impact craters provide the richer information on the complicate petrology of deep-seated geospheres which cannot be obtained on the base of laboratory experiments.
New Minerals. LXXVII
Authors: Smolyaninova V. N.
Published: April 2024

The paper displays review of new minerals published in 2022. Data for each one mineral include its crystal-chemical formula, unit cell parameters, principal physical properties, chemical composition, type locality, etymology of its name, reference of the first publishing about it. In total, the review includes data on 106 newly discovered minerals approved by the IMA. There are also references for publications on questions of classification and nomenclature of minerals, improvements of composition and structure of known mineral species.
The Possibility of Using Modern Methods and Data to Study the Spatial Structure of the St.-Petersburg Agglomeration
Authors: Lachininskii S. S. , Logvinov I. A. , Sorokin I. S.
Published: April 2024

Abstract—The article is devoted to the review and substantiation of modern research methods and data sources on the dynamics of spatial structure of the largest Russian urban agglomerations. The object of the study is modern methods and data sources, and the subject is the possibilities of their use. On the example of the second agglomeration in Russia – St.‑Petersburg urban agglomeration – it is shown that interdisciplinary synthesis within the framework of socio-economic geography, regional economics, urban studies, geoinformatics and cartography, land management, using a variety of data sources (data of cellular operators, tax statistics, housing construction, satellite data, retail chains, road network), as well as the use of modern GIS-complexes, allow us to assess this structure, its changes, as well as to analyze the spatial structure of the largest Russian urban agglomerations. The main objective of this study is to review and critically rethink the methods of studying the spatial structure of one of Russia’s largest urban agglomerations (St.-Petersburg) developing in the turbulent period between 2014 and 2022. An inventory of different methods and data sources was made, using the method of reasoning. Further, the advantages and disadvantages of each group of methods were identified. Through an in-depth bibliographic analysis, the limitations and possibilities of empirical content (availability of specific data sources) were identified. Based on the critical analysis of advantages and disadvantages, a final point estimate of applicability and usefulness of the considered methods for the St. Petersburg urban agglomeration is obtained. The author’s contribution lies in the adaptation of modern groups of methods for the study of the spatial structure of cities for the study of the considered agglomeration, taking into account the local specificity and assessment of applicability and usefulness of the considered methods for St. Petersburg urban agglomeration. It is assumed that the development of a modern methodology for studying the spatial structure of the St. Petersburg urban agglomeration based on the symbiosis of modern methods and data sources will make a certain contribution to the study of the largest Russian agglomerations.
Geochemical Characteristics Infiltration Deposits Kungur Ice Cave (Preduralie)
Authors: Lavrovа N. V.
Published: April 2024

Abstract—The results of spectral analyses of infiltration deposits of a large karst system in carbonate-sulfate deposits are presented. The movement of loose material from the surface through deformation zones within an array with a capacity of 80–90 m leads to accumulations of gravel-clay deposits in the lower part of grottoes and galleries. The localization of deposits is confined to certain forms of underground karst relief – organ pipes: vertical structures up to 20–25 m high, free or filled with debris. Regularities in the distribution of individual oxides and elements are revealed, their values are compared with residual deposits, as well as matrix rocks. Infiltration waters entering the karst massif in the pre-paleogenic stage determined the conditions for the formation of cryogenic minerals during the freezing of rocks. The cyclical nature of the material intake is compared with the periods of Late Pleistocene climatic events.
Scientific Support of Gully Rehabilitation in Protected Landscapes
Authors: Solodyankina S. V. , Vanteeva Yu. V. , Opekunova M. Yu. , Rybchenko A. A. , Kozyreva E. A. , Mazaeva O. A. , Znamenskaya T. I. , Yuriev А. А.
Published: April 2024

Abstract—The experience of scientific support of work on the rehabilitation of the gully on the Cape Burkhan on the Olkhon Island (south of Eastern Siberia, Lake Baikal) is considered in this article. Cape Burkhan is a unique natural monument with a recognizable landscape and a high-status tourist attraction, which is exposed to a high recreational impact. The processes of linear erosion develop in this area most intensively due to the characteristics of the lithological and geological structure and morphological parameters. The anthropogenic factor has the greatest influence on the activation of dangerous geomorphological processes, including erosional ones. As a result of the study, the comprehensive analysis of the territory was carried out: initial conditions, causes, and factors of vegetation and soils degradation, activation of erosion processes. Various approaches to the technological and biological stages of gully rehabilitation were analyzed. Detailed recommendations have been developed to reduce the recreational impact on the relief and carry out restoration work. The proposed approaches to rehabilitation can be used on other gullies on Olkhon Island and the Priolkhonskoe plateau.