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
This paper analyzes the reflection of unsteady long waves from a straight vertical wall in a homogeneous fluid of constant depth under rotation, with the Coriolis force included. Starting from the linear long wave equations, the authors formulate an initial value and boundary value problem for a loc…
This paper derives sufficient conditions for using Euler’s static method to study the stability of deformation of isotropic nonlinearly elastic bodies under finite subcritical deformations. Starting from the linearized equations and boundary conditions in Lagrangian coordinates for a body with an ar…
The paper constructs exact non-self-similar triple-wave solutions for the equations of potential unsteady gas dynamics in a polytropic gas with adiabatic exponent between 1 and 2. It seeks the sound-speed function and placement potential in a special algebraic-functional form, reducing the overdeter…
This paper investigates how the form of regular surface perturbations affects the breakup of low-viscosity liquid jets into drops, with particular attention to suppressing satellite microdrops. Experiments with water and molten ammonium nitrate used pressure pulses from an oscillating membrane to va…
This paper examines how discrete admixtures of solid particles or liquid droplets alter the structure and spreading of a turbulent gas jet. Using Prandtl mixing-length theory and momentum balance for turbulent eddies containing particles, it derives estimates for the reduction of pulsation velocitie…
This paper treats the direct problem of unsteady and steady ideal-gas flow in Laval nozzles of prescribed geometry, including subsonic, transonic, and supersonic regions. The authors formulate the gas-dynamic equations in transformed coordinates and describe a finite-difference marching algorithm wi…
This paper studies self-similar dynamic plane-strain elasticity problems for an infinite isotropic body containing a rectilinear crack that begins at a point source and expands at constant subsonic velocity. Using displacement potentials and the Smirnov-Sobolev transformation, the boundary condition…
The paper treats the three-dimensional equilibrium problem for an elastic body bounded by two parallel planes and subjected to arbitrary surface and body forces. It reduces the loading to components satisfying integral balance conditions, formulates auxiliary equations for polynomial displacement te…
This paper studies nonlinear interaction in resonant conservative Hamiltonian systems with multiple degrees of freedom, assuming a single resonance relation among distinct linear frequencies. Using a polynomial canonical transformation, the authors reduce the Hamiltonian to a resonant normal form up…
This paper studies the one-dimensional reflection of a rarefaction wave from a rigid wall in the products of an instantaneous explosion in a constant gravitational field, for a gas obeying a polytropic equation of state. Starting from the general solution of the gas-dynamic equations for discrete ad…
The paper examines passage through the self-oscillation zone of a rigid rotor rotating in journal bearings, focusing on the use of elastic supports rather than specially shaped vibration-resistant bearings. A nonlinear model is formulated for a symmetric rotor in elastic journal bearings, and, for a…
The paper develops an asymptotic averaging method for nonsinusoidal waves in arbitrary nonlinear first-order partial differential systems, including cases with slow inhomogeneity, nonstationarity, and possible nonconservative terms. Starting from a family of periodic stationary plane-wave solutions,…
This paper studies steady finite-amplitude capillary-gravity waves on an ideal incompressible liquid of infinite depth, forced by a periodic pressure distribution on the free surface. Using conformal mapping, Bernoulli’s condition with surface tension, and Dini relations, the boundary-value problem …
This paper develops a method for solving boundary value problems arising in the stability analysis of axisymmetric equilibrium states of circular cylindrical shells. After separation of variables, the problem is reduced to a homogeneous system of ordinary differential equations with exponential coef…
This paper studies convergence of the method of “elastic” solutions for quasistatic boundary-value problems in a principal quasi-linear incompressible viscoelastic medium with small strains. The problem is formulated in a Hilbert space of generalized displacements, using integral identities for the …
This paper examines the hydraulic resistance of granular porous media during colmatation caused by filtration of dilute suspensions, a problem relevant to water treatment and other filtration technologies. The authors describe experiments in which dynamic porosity was measured without disturbing dep…
The paper derives integral representations for solutions of the differential equations in the technical theory of shallow shells, focusing on the case with constant curvature parameters after transformation to complex variables. The governing coupled shell equations are reduced to a fourth order equ…
The paper studies the asymptotic deflection of a finite viscoelastic beam of variable cross-section resting on a Winkler elastic foundation, with hereditary material behavior represented by an integral kernel. Using Tauberian theorems of Paley, Wiener, and Gelfand type, it derives conditions under w…
This paper investigates whether internal shock waves can occur in axisymmetric supersonic flow of a perfect gas past cones with spherical blunt noses and no break in the generatrix at the junction. Using finite difference calculations of the steady flow near a sphere, subsequent supersonic flow comp…
The paper studies the stability of time-periodic forced motions of a viscous incompressible fluid in a bounded three-dimensional domain, formulated through perturbations of a periodic Navier-Stokes solution in an energy space. It establishes well-posedness and compact differentiability properties fo…
This paper applies the principle of maximum stability to determine the mean velocity profile in the viscous sublayer and buffer region of turbulent channel flow. Using a generalized Van Driest mixing-length formula with adjustable parameters, the authors analyze local hydrodynamic stability of short…
This paper presents a numerical study of the onset and structure of natural convection in water near its temperature of maximum density, where density depends quadratically on temperature rather than linearly. A two-dimensional stationary problem is solved for a viscous liquid in a square cavity hea…
This paper examines how nonuniform stiffness in elastic ring supports can induce parametric oscillations in a rigid rotor mounted on one elastic and one hinged support. The authors formulate linear equations for small forced oscillations including gyroscopic effects, viscous damping, rotor unbalance…
The paper studies periodic convolution equations arising in mixed problems of elasticity, especially contact problems for finite bodies, in cases where the interval length is not assumed small relative to the period. For kernels with Fourier coefficients of order inverse linear decay, it establishes…
This paper addresses how to determine positions of a machine unit’s reduction link at which the characteristic criterion of a periodic limiting regime reaches extrema, indicating where inertia forces due to nonuniform initial motion are most significant relative to steady motion. Under standard assu…
This paper extends analytic function and contour integral methods for three-dimensional elasticity from bodies of revolution to certain non-axisymmetric bodies whose surfaces can be represented as envelopes of a moving cylindrical surface. The method superposes plane strain and antiplane deformation…
This paper examines how specular reflection of vapor molecules from capillary walls can alter gas transport in narrow capillaries, producing a flow regime distinct from ordinary Knudsen flow. The authors develop a model in which molecules reflected below a limiting angle have an increased transport …
This paper formulates equations of nonlinear elasticity in terms of displacements for finite deformations, using Green, Almansi, and Hencky strain tensors together with true and generalized stress tensors. It derives variational relations, stress potentials, boundary conditions, and constitutive law…
This paper analyzes the dynamics of a rigid unbalanced rotor supported by rolling bearings with preliminary axial preload, a configuration used in high-speed precision assemblies to increase stiffness and reduce clearance effects. An analytical relation is derived between axial spring stiffness and …
This paper addresses the difficulty of solving boundary value problems in shallow shell theory caused by the lack of complete systems of solutions for the governing equations. Using integral representations of the general solution, it constructs families of regular solutions expressed through comple…
The paper formulates finite plane deformation problems for an ideally elastic isotropic body in complex coordinates of the initial configuration, without imposing geometric or physical linearization. It derives geometric compatibility relations in terms of logarithmic strain invariants and rotation,…
The paper analyzes the limit equilibrium of reinforced shells resting on a rigid-plastic foundation, for shells whose horizontal sections have similar polygonal or limiting curvilinear projections. Using a virtual work formulation for an assumed plastic mechanism with horizontal plastic hinges and c…
This paper introduces the hysterant operator as a mathematical tool for describing hysteresis-type nonlinearities arising in Prager-Ishlinskii models of elastic-plastic behavior. The authors define an elementary hysterant first for continuous piecewise-linear inputs and then extend it to arbitrary c…
This paper studies the time-dependent size of plastic zones in elastic-plastic bodies with aftereffect, focusing on a hollow sphere under internal and external pressure and related axially symmetric cylinder problems. Using operator constitutive relations for shear, volumetric response, and hardenin…
This paper investigates camouflet cavity formation produced by spherical explosive charges in liquids and elastoplastic media, including water, zinc chloride solution, wet clay, aluminum, cement and sand mortar, and rock salt. The authors combine pulsed radiographic measurements of cavity expansion …
This paper develops a linearization principle for the stability of periodic self-oscillations in infinite-dimensional dynamical systems, formulated as nonlinear partial semigroups on a Banach space. It proves an analogue of the Andronov-Witt theorem: a smooth cycle is asymptotically stable with asym…
This paper develops a calculation method for the stable roughness that forms after running-in during sliding elastic contact. Using the molecular-mechanical theory of friction together with a fatigue interpretation of wear, the authors argue that the stable surface state corresponds to the roughness…
This paper studies the spectral problem arising from the membrane approximation to axisymmetric vibrations of a shell of revolution with clamped edges, obtained by setting the small thickness parameter to zero in the shell equations. The authors formulate the associated self-adjoint operator, analyz…
This paper develops a generalization of Mindlin’s method for elasticity problems in a half-space by using analytic continuation of elastic solutions through a plane boundary. It formulates reflection laws for body forces that allow boundary-value problems with either vanishing displacements or vanis…
This paper analyzes the dynamic buckling of cylindrical fiberglass shells treated as orthotropic under axial impact by a finite striking mass, including the effect of initial geometric imperfections. The authors formulate the problem using nonlinear shell equations, approximate rhomboidal dent shape…
This paper proposes a variant of the method of successive approximations for numerical integration of two-dimensional incompressible Prandtl boundary-layer equations with an arbitrary pressure gradient, assuming that a solution exists. The method integrates the momentum equation with respect to the …
This paper examines stresses arising during axisymmetric buckling of thin spherical shell segments, focusing on an experimental check of a previously derived formula relating stress to shell thickness, local bending geometry, and material properties. Instead of measuring stress directly, the study m…
The paper studies quasistatic boundary value problems in the linear theory of thermo-viscoelasticity with contact-type boundary conditions, using operator notation based on relaxation and creep kernels and the Laplace-Carson transform. It establishes uniqueness under standard positivity conditions o…
An asymptotic method is developed for weakly nonlinear one-dimensional distributed systems with dispersion, aimed at problems of wave propagation and interaction where expansions in normal modes with time-dependent parameters are insufficient. The approach represents multiwave quasiharmonic solution…
This paper develops a mathematical model for dynamic buckling of a finite thin circular cylindrical shell subjected to a localized axisymmetric thermal shock near one end. The formulation couples one-dimensional thermoelastic equations for temperature and axial displacement with geometrically nonlin…
The paper extends V. V. Novozhilov’s method of complex transformation from the Kirchhoff Love thin shell theory to the linear theory of elastic shells of Timoshenko type, in which transverse shear deformations are included. Starting from the kinematic, equilibrium, constitutive, and compatibility re…
The paper studies stability in the spatial three-body problem for two planets in canonical variables, with particular attention to the behavior of the slowly varying action variables near resonance lines where integer combinations of mean motions vanish. Using a generalized form of Lyapunov’s second…
This paper examines how Lagrangian invariants of inviscid compressible fluid dynamics can be systematized and generated for barotropic, adiabatic, and isothermal models. Using generalized Weber and Clebsch representations, the authors argue that the Eulerian fields of an adiabatic fluid can be deter…
This paper studies limiting modes of motion for machine units whose reduced force moment depends on the driving angle and kinetic energy and may have piecewise-monotone characteristics with discontinuous slope. Using the kinetic energy equation, it establishes conditions for the existence of inertia…
This paper analyzes steady-state dynamic vibrations of an infinite elastic plane containing a finite crack subjected to a harmonic normal load on the crack faces. Using elliptic coordinates, the displacement potentials are reduced to Mathieu equations, and the boundary conditions on the crack are tr…
