SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 813 papers in Mechanics
The paper formulates the nonstationary problem of axial impact of a finite viscoplastic rod against a rigid barrier, treating the motion as quasi-one-dimensional and separating the rod into viscoplastic and rigid regions divided by a moving boundary. By nondimensionalizing the governing relations, t…
This paper analyzes supersonic flow of a weakly relaxing gas past a wedge, with particular attention to vibrational relaxation behind an oblique shock. By linearizing the gas-dynamic equations with a relaxation term and solving the resulting boundary-value problem, it derives exact series expression…
This note derives an expression for the evolution of potential vorticity in a stratified fluid subject to weak external influences, including heat influx and frictional forces. Starting from the hydrodynamic equations, continuity equation, equation of state, and a prescribed entropy change, it shows…
The paper develops a simplified model for spherically symmetric fracture in a solid whose tensile strength is much lower than its compressive strength, focusing on the formation of a densely cracked radial zone behind an outgoing elastic wave. It assumes that radial cracks instantaneously relieve az…
The paper formulates an approximate elastic stability problem for a vertical cylindrical mine working of circular cross section in a homogeneous isotropic rock mass. Starting from a known elastic stress and displacement field, it treats buckling as a perturbed equilibrium problem for an annular laye…
This paper addresses the statistical distribution of elastic constants in quasi-isotropic, single-phase polycrystals, where crystallographic orientations are random at the microscopic scale. The authors formulate the elastic-constant transformation in terms of Euler angles and derive the joint densi…
This paper examines whether geometric nonlinearity remains important in the stability of cylindrical shells compressed beyond the elastic limit. Thirty closed circular cylindrical shells of duralumin alloy with length to radius ratio 2 and radius to thickness ratios from 25 to 135 were tested under …
This paper analyzes coherent and incoherent acoustic scattering from a deep-water layer containing randomly distributed discrete inhomogeneities, addressing cases where scatterer spacing is comparable with the wavelength and interference cannot be neglected. Using statistical averaging over scattere…
The paper formulates the manifestation of rock pressure in deep horizontal workings as a stability problem for an elastic-plastic rock mass surrounding a circular opening. Assuming an initially hydrostatic stress field, a Coulomb-type plasticity condition, and an elastic region outside a plastic zon…
This paper examines how elasticity in the supports of the outer ring axis of a Cardan suspension affects nutational oscillations and gyroscope drift. Starting from the inertial equations for a balanced gyroscope, it uses an added-degree-of-freedom formulation to compute support reaction moments and …
This paper develops a spectral description of weak inhomogeneous turbulence in incompressible viscous flows, focusing on how nonuniform mean motion can amplify turbulent fluctuations. Starting from averaged Navier Stokes equations and neglecting higher order correlations in the initial approximation…
This paper examines how the free surface of water in a glass vessel changes as effective gravity is reduced to zero, a problem motivated by observations of liquids during spaceflight. Using capillary equilibrium equations for a wetting liquid in a cylindrical vessel, the author relates meniscus prof…
The paper extends a method based on functions conjugate on the contour from stress problems to displacement boundary value problems for an infinite elastic strip. Using Kolosov’s complex-variable equations, it formulates four symmetric and antisymmetric deformation cases and reduces the prescribed b…
This paper develops a thermodynamic framework for constructing nonholonomic continuum models that account for finite deformations, temperature effects, residual deformation, creep, relaxation, and related physicochemical processes. The authors introduce, alongside strain, stress, and temperature, an…
This paper generalizes Huygens’ reciprocity theorem for the physical pendulum to a heavy rigid body undergoing Hessian motion about a fixed point. It introduces the kinetic axis and kinetic center of the body, relates them to the central axis of the momentum screw, and analyzes the Hess structural c…
This paper analyzes the propagation of gravity and capillary surface waves on an ideal incompressible conducting liquid in a uniform external magnetic field, using linearized magnetohydrodynamic equations under the assumption of small wave amplitude and effectively infinite conductivity. For a field…
This paper analyzes nutational oscillations and drift in a synchronous gyroscope mounted in a gimbal suspension when the gimbal rings are not perpendicular and the stator magnetic field torque affects the motion. Using Lagrange equations, the study derives equations of motion, first integrals, stabi…
This paper proposes a mathematical model for separated flows of an incompressible ideal fluid in which the flow is potential outside a separation region and has prescribed constant vorticity inside it. The model is formulated through a stream function satisfying a nonlinear free boundary problem, eq…
This paper addresses the experimentally observed S-shaped dependence of combustion velocity on component particle size in condensed mixtures whose components gasify before mixing, a behavior not adequately described by one-dimensional theories. The authors propose a simplified nonuniform combustion-…
This paper develops a continuum elastic theory for binary interstitial solid solutions in which impurity atoms may occupy several nonequivalent interstitial positions, with emphasis on a body-centered cubic lattice. The authors formulate the free energy in terms of strain and position-dependent impu…
The paper develops an asymptotic scheme for studying a class of gyroscopic systems described by two coupled second order equations with small perturbing terms. A solution is represented through slowly varying amplitude, phase, and mean coordinates, with periodic correction functions, and conditions …
The paper derives equations of motion for the basic body in a system composed of rigid bodies of variable composition connected in open kinematic chains, where mass loss occurs through separation of particles from instantaneous outer surfaces. Using matrix notation for masses, inertia tensors, relat…
The paper formulates a variational principle for the nonlinear theory of elasticity in which displacements, stresses, and strains are treated as independently varied quantities without imposing internal or boundary constraints in advance. By computing the first variation of a proposed functional, th…
This paper studies the onset of asymmetric deflection, or corrugation, in a circular plate that is rigidly supported and uniformly compressed along its boundary without transverse loading. The plate is formulated through the Kirchhoff equations and an associated energy functional, whose stationary p…
A method is presented for solving statically indeterminate plane flow problems of ideally plastic bodies when the arrangement and number of plastic regions are known. The approach uses the velocity field on the characteristic plane to derive the missing stress boundary conditions, with Riemann’s for…
This paper examines buckling surfaces associated with local loss of stability in thin circular cylindrical, conical, and spherical shells under compression or external pressure. It proposes a method that separates determination of the buckling form from determination of the critical load, using nonl…
This paper analyzes the local elasto-plastic stress state that develops during torsion of a rod with a small semicylindrical longitudinal surface groove, assuming a strain-softening material. The grooved rod is modeled near the recess as an elastic half-space with a semicylindrical notch, and the el…
This paper studies the initial boundary value problem for an ideal incompressible fluid in a bounded two-dimensional domain with a permeable boundary, where prescribing only the normal velocity is insufficient for uniqueness. It proposes an additional boundary condition on the vorticity at inflow po…
This paper develops a simple energetic estimate for the dynamic yield shear stress of suspensions whose colloidal particles possess rigid electric dipole moments. Assuming a locally ordered, cubic-like arrangement of dipolar particles, the authors relate the work required to shear adjacent particle …
This paper studies the large convective parameter asymptotics of the solution to an axisymmetric thermoconvective contact boundary value problem previously represented by double Laplace, Carson and Hankel transforms. For the case of unit diffusivity parameter and integer convective parameter, an exa…
This paper estimates the relaxation time for carbon dioxide dissociation using shock-tube measurements of reflected shock waves in carbon dioxide containing a small amount of water vapor. The analysis compares observed reflected-wave velocities with values calculated for frozen and equilibrium disso…
This paper applies an asymptotic approximation method for systems with a rotating phase to the dynamics of the Boussinesq-Sardeau regulator, a device intended to ensure uniform lowering of a suspended load. The general averaging procedure eliminates the fast phase from a system of differential equat…
This paper develops a theoretical treatment of deposition of highly dispersed aerosol particles from a slow gas flow onto an ultrathin stationary cylinder whose radius may be comparable to or smaller than the molecular mean free path. Using the convective diffusion equation with a concentration jump…
This paper studies heating and melting of a solid body caused by friction with a high-velocity viscous liquid flow in a formulation that, unlike earlier work, does not admit a self-similar solution. The moving boundary problem is posed for the solid, melt, and surrounding liquid, including heat cond…
The paper examines which small dissipative terms can be added to the equations of isothermal gas motion while still yielding physically admissible discontinuous solutions in the inviscid limit. It proves that a triangular constant viscosity matrix with positive diagonal entries and any nonzero off-d…
This note examines the post-critical elastic state of hinged cylindrical shells subjected to torsion, focusing on deformation after loss of stability and the associated upper and lower critical loads. The analysis models post-critical shapes as isometric bendings with periodic structure inherited fr…
This paper studies the propagation of an initially localized elevation of a long wave in an infinitely extended rotating basin with piecewise constant depth, including a finite ledge bounded by two depth discontinuities. The tidal equations with continuity of surface elevation and discharge at the d…
This paper studies the large time behavior of surface waves in a heavy liquid of finite depth generated by an arbitrary initial elevation of the free surface, with attention to waves propagating near the maximal velocity where standard stationary phase formulas are inadequate. Using the linear theor…
The paper studies a nonlinear boundary-value problem for analytic functions in the upper half-plane, motivated by elastic-plastic problems, with boundary conditions prescribing either the modulus of the unknown function or a real linear relation on complementary parts of the real axis. It reduces th…
This paper examines how strong electric fields affect the structure and rheological behavior of nonaqueous plastic disperse systems, using hydrated calcium grease and sodium soap-thickened lubricants as examples. The authors combine polarized-light microscopy with experiments in a plastoviscosimeter…
This paper justifies Dirichlet’s principle for the first boundary-value problem in a class of nonlinear elasticity models where the deviators of strain and stress are related by a hardening law. The argument formulates the displacement problem as minimization of a uniformly convex energy functional …
This paper examines how small velocity-dependent friction affects the critical load and stability boundary of a compressed cantilever rod subjected to end weight and a follower force. Using a two-degree-of-freedom model with end deflection and rotation as generalized coordinates, the authors derive …
The paper analyzes the stability loss of a thick rectangular simply supported plate uniformly compressed in one direction, treating the material as incompressible and plastically deformable. It formulates the problem using elastic-plastic flow theory for an anisotropically hardening material, derive…
This paper presents a method for determining periodic motions in one degree of freedom conservative systems governed by a nonlinear autonomous second order equation. By shifting the coordinate origin and representing the potential integral as a polynomial, the method rewrites the first integral in a…
This paper examines how the yield strength of several structural metals changes under combined low temperatures and high loading rates, with attention to implications for brittle fracture. Using oscillographic recording of the transition from elastic to small plastic deformation, and additional test…
This paper considers rarefied gas flow past a flat plate of arbitrary planform in the regime close to free molecular flow, where first collisions between incident and reflected molecules are taken into account. Using influence functions for the changes in particle flux, momentum, and energy contribu…
This note formulates the problem of liquid motion of infinite depth produced by a strong explosion at a free surface, treating the liquid as incompressible after the shock wave has departed. It compares two possible self-similar descriptions, one using explosion energy as the determining parameter a…
This paper investigates the curvature of linearly enveloping cycloidal curves generated by mechanisms with rolling circular centrodes and an enveloping straight line. Using the Euler-Savary relation and comparing with Bobillier’s construction, it derives formulas for the radius of curvature and the …
The paper addresses the determination of stress and strain tensors during repeated proportional loading of an elastic-plastic medium that exhibits cyclic hardening under symmetric or nearly symmetric cycles. It models the decrease of plastic strain components with loading number by introducing a mat…
This paper examines the reflection of a weak discontinuity in transonic flow from a sonic line when the jump in velocity derivatives has the sign not treated in earlier work. Using the Euler Tricomi equation in hodograph variables, the authors analytically continue the incident singular solution, an…
