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 proposes a thermodynamic framework for relations between stresses and strains in inelastic continuous media, extending phenomenological elasticity by introducing additional internal state parameters associated with hidden internal stresses and irreversible deformation. Starting from the e…
This paper examines which equations of state permit one-dimensional motions with homogeneous deformation, extending earlier treatments that assumed a perfect gas. Starting from the momentum equation under the deformation condition and considering either adiabatic motion or spatially uniform temperat…
This paper studies the stability and natural oscillations of a thin elastic plate moving at supersonic speed, using linearized aerodynamic theory and small-deflection plate assumptions. The coupled aeroelastic problem is reduced to an integro-differential equation for the plate deflection, reformula…
This paper studies small unsteady disturbances produced by a thin wing of finite span moving in an unbounded compressible fluid, with an arbitrary prescribed law of motion and possible additional surface deformations. The problem is formulated as a linear boundary-value problem for the three-dimensi…
This paper examines the critical Stokes number for inertial deposition of aerosol particles in viscous flow around a cylinder and a sphere, emphasizing that a formula valid for potential flow cannot be applied to viscous flow because the no-slip boundary condition makes the relevant velocity gradien…
This note extends the idea of conjugate problems from plane elasticity to the theory of thin shells. Under simplifying assumptions for a homogeneous shell with boundary along a line of curvature and zero Poisson coefficient, it introduces complex combinations of displacements, stresses, moments, and…
This paper develops a method for estimating maximum shear stresses in the bending of prismatic cantilever bars whose cross sections are symmetric with respect to the axis of loading. Using a complex bending function and properties of subharmonic functions, it derives integral relations for tangentia…
This paper studies existence and uniqueness questions for the nonlinear theory of elastic shells in a general setting, extending earlier results for shells close to plates under transverse loading. The shell equations are formulated with clamped boundary conditions and interpreted through generalize…
This paper examines surge in compressor and fan systems as a nonlinear self-oscillation problem, focusing on the conditions for excitation, the character of oscillations, and possible suppression. Using a reduced one-degree-of-freedom acoustic model with compressor and network characteristics, it de…
The paper studies unsteady two-dimensional laminar flow of an incompressible viscous fluid between parallel porous walls, extending earlier steady-flow treatments to the case where wall permeability varies with time while a constant flow parameter is assumed. Using a separated stream-function form, …
This paper examines gas dynamic motions of an aerosol modeled as a gas containing many small, light particles or droplets that move with the carrier gas and increase the effective inertia and heat capacity of the medium. It shows that, under these assumptions, the usual hydrodynamic equations, adiab…
The paper studies harmonic heat waves in a thin unbounded plate whose temperature is assumed uniform through the thickness, with convective exchange on the upper face and contact with a continuous homogeneous foundation on the lower face. Using sinusoidal spatial and temporal heat sources, it formul…
This study investigates the kinetics of rupture growth in unfilled nitrile rubber vulcanizates in the high elastic state, focusing on the effects of notch size, deformation rate, stress, and cohesive energy. Rectangular specimens of SKN-18, SKN-26, and SKN-40 with controlled cuts were stretched at s…
The paper develops Prandtl’s proposed “second” form of ideal-fluid motion past sharp-edged streamlined bodies, in which separated flow is represented by vortex sheets and spiral surfaces of tangential velocity discontinuity. It decomposes such flows into a basic potential flow and an additional vort…
This paper treats the classical plane strain problem of stress and strain distribution in an infinite plane acted on by a concentrated force, reformulated for elastic-plastic deformation. Assuming material incompressibility and a linear hardening law in the plastic region, the author derives stress …
The paper develops an approximate method for plane problems in the theory of small elastoplastic deformations by expanding stresses, displacements, and strains in a parameter about an axisymmetric zeroth-order state, with incompressibility and a power-law relation between stress and strain intensiti…
This paper studies infinitesimal bendings of surfaces and their relation to momentless stress states in thin shells, with emphasis on boundary constraints that are compatible with such bendings and have well-posedness properties. It formulates the correspondence between bending fields and momentless…
This paper formulates the problem of plane supersonic ideal-gas flow past a circular cylinder with an initially unknown detached shock wave, including boundary conditions on the body and shock. It applies the method of integral relations, replacing the flow region between the body and shock by a fin…
The paper studies unsteady isentropic gas flows in plane and spatial settings, with emphasis on self-similar motions in which the variables depend on spatial coordinates divided by time. Starting from the Euler equations and, for plane flows, the potential-flow formulation, it derives transformed eq…
The paper formulates a generalized model for radial displacement of gas-saturated oil by water in a circular reservoir, allowing for pressure-dependent oil and gas properties, deviations from ideal gas behavior, and changes in oil formation volume factor during degassing. Using material-balance rela…
This paper presents the theory of a two-degree-of-freedom kinematic chain that transforms the path of one point into the path of another. It derives the coordinate relation for the transformer, \(x=\xi\) and \(y=\xi^2/\eta\), and shows that the transformation is reversible. Several cases are analyze…
This note gives an exact solution for the one-dimensional adiabatic motion produced by an instantaneous release of finite energy in a gas whose initial pressure is constant and whose initial density varies with distance according to a specified parametric law. The problem is formulated for spherical…
The paper studies the motion of a rigid body about a fixed point in a central Newtonian force field, assuming the fixed point is far from the attracting center relative to the body’s dimensions. It derives approximate equations of motion in principal axes and identifies first integrals, showing that…
This paper studies accelerations of arbitrary order for a rigid body in plane-parallel motion, using Somov’s generalized formulas in matrix form and recurrence relations for the coefficients governing rotational motion. It defines reduced accelerations of order n and establishes several geometric pr…
This paper examines deviations from the Stefan, Reynolds description of liquid flow in very narrow gaps between approaching or separating plane parallel disks. Using a method that measures disk separation time and gap thickness down to submicron scales, it studies mineral oils, fatty acid solutions,…
This paper analyzes the evolution of small nonstationary discontinuities in a one-dimensional relaxing medium, where relaxation processes introduce distinct low-frequency and high-frequency sound speeds. Using linearized hydrodynamic equations with a single relaxation time, the authors solve the pis…
This note formulates the contact problem for a punch resting on an elastic foundation with a homogeneous axisymmetric kernel, reducing the determination of the unknown pressure distribution to a system of dual integral equations. It then treats the case in which the modulus of elasticity of the half…
This paper treats the elastic bending of a homogeneous isotropic prismatic bar of square-like cross section weakened by a circular cavity, under a concentrated force applied along a minor axis. Using complex-variable methods in elasticity, the boundary-value problem is reduced to the construction of…
This paper derives the equations of a three-dimensional boundary layer in a viscous compressible gas over an arbitrary smooth surface. Using orthogonal curvilinear coordinates based on the surface lines of curvature, the author applies boundary-layer scaling at large Reynolds number to the compressi…
The paper formulates a variational problem for determining the generator of a body of revolution with minimum wave drag in axisymmetric supersonic flow, and an analogous nozzle problem with minimal losses. Using a characteristic representation due to Nikolskii, the drag functional is optimized under…
This paper develops a formulation for the elastic equilibrium of bodies of revolution under loads expanded in Fourier series with respect to the circumferential coordinate. Assuming harmonic forms for the displacement components, the equilibrium equations are reduced to auxiliary stress functions sa…
This note addresses uniqueness for the boundary value problems arising in successive approximations to the dynamics and heat exchange of an incompressible fluid whose viscosity varies with temperature. For prescribed viscosity, it proves uniqueness of the velocity field, with pressure determined up …
This paper examines how initial geometric imperfections affect the large-deflection stability of a hinged circular cylindrical shell under uniform external pressure. Using a Ritz approximation for the shell deflection that includes circumferential waves, inward bulging, and radial displacement of th…
This paper studies an automodel problem for diffusion of a vortex layer and heat transfer in a half-space liquid whose viscosity, thermal conductivity, and heat capacity may depend on temperature. The governing momentum and energy equations, including viscous dissipation, are reduced by dimensional …
This paper studies high supersonic gas flow past a thin cone with a blunt nose, extending an earlier approximate formulation for blunted wedges to axisymmetric bodies. The blunt nose is represented by a concentrated drag force, and the flow is reduced, using the law of plane sections, to a one-dimen…
This paper examines a bifurcation of stationary motion in which the principal form does not lose stability, contrasting it with familiar examples such as Euler buckling and the rotating pendulum. Motivated by experiments on an elongated axisymmetric rigid body suspended by a string, it formulates th…
This paper applies Volterra’s integral method to the linearized problem of supersonic flow past axisymmetric surfaces that differ slightly from a circular cylinder. Through transformations of the Volterra representation, the boundary-value problem is reduced to a linear Volterra integral equation of…
This paper derives similarity integrals for equations describing plane viscous gas flows coupled with heterogeneous surface reactions and homogeneous volume reactions, under incompressible low-speed assumptions and unit diffusion number. For heterogeneous reactions, it introduces a combined concentr…
This paper derives an asymptotic solution for one-dimensional unsteady motion of an ideal gas with cylindrical symmetry, extending characteristic-variable methods previously applied to shock-wave attenuation. The solution represents direct and reflected waves, together with their interaction, as ser…
The note generalizes earlier reductions of plane-parallel steady vortical gas motion to potential flow beyond the separable velocity form. It considers velocity functions for which the ratio of the second pressure derivative to the velocity is independent of the stream function, implying a two-term …
This paper studies small oscillations of multiple rigid bodies floating on the surface of a liquid contained in a bounded basin, within linear wave theory. It formulates coupled equations for body translations and rotations and the free surface elevation using added masses, Green’s functions, and no…
This note studies the first boundary value problem in nonlinear elasticity, with the displacement prescribed on the boundary, in both three-dimensional Sobolev spaces and plane Hölder spaces. It formulates the nonlinear elasticity operator, relates the method of elastic solutions to a modified Newto…
This paper applies Dorodnitsyn’s approximate numerical method for reducing two-dimensional nonlinear gas-dynamic problems to ordinary differential equations to the flow of a sonic gas stream past ellipses. The mixed potential motion upstream of the boundary characteristics is formulated in elliptic …
This paper proposes a plasticity theory for quasi-isotropic bodies that incorporates the Bauschinger effect by distinguishing actual stresses from active stresses and introducing a tensor of residual stresses. The yield surface retains the spherical form used in flow theory, but its center moves dur…
This paper extends a previous study of ideal-fluid separated flow in which tangential discontinuity surfaces form near bodies, focusing on the additional pressure forces produced by this “second” form of hydrodynamic motion. Using complex potential methods, it derives a superposition rule for the fo…
This paper studies the transient response of an infinite elastic plate resting on an elastic liquid half-space under a point impulse, initially represented as a spatially and temporally distributed load and then obtained by a limiting process. The plate vibration equation is coupled to a wave equati…
This paper develops an approximate treatment of plane, unsteady potential motion of an incompressible fluid with a free surface in a narrow channel. Using Lavrent'ev's conformal mapping formula for narrow regions, it derives asymptotic evolution equations for the free surface and velocity potential,…
This paper analyzes steady filtration through a very high rectangular cofferdam when the capillary rise is also taken to be very large and the capillary zone is fully saturated. Using a complex potential formulation, conformal mapping, and Christoffel-Schwarz transformations, it derives integral rel…
This paper treats diffraction of an obliquely incident plane sound wave by a thin finite elastic cylindrical shell hinged into a rigid cylindrical screen. Using Green’s theorem, radiation conditions, and equality of normal velocities at the fluid, shell boundary, the acoustic field is represented by…
This paper analyzes how a small bluntness at the leading edge of a thin airfoil or wedge can alter high supersonic flow over distances much larger than the bluntness size. The effect of the blunt edge is modeled as a concentrated force at the leading point, and the steady aerodynamic problem is redu…
