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 develops a statistical justification for equations describing filtration motion in porous media, treating observed filtration velocity as a cross-sectional average over many local pore-scale liquid jets. By averaging local Navier-Stokes motion and using a pore-size distribution, it derive…
This paper develops an approximate theory for the impact of arbitrary cylindrical elastic bodies when their initial contact has order greater than one, extending earlier work on equal circular cylinders. The analysis combines a static contact pressure distribution with a dynamic treatment of displac…
This note treats the reflection and refraction of nonstationary elastic waves of arbitrary form at a smooth curvilinear interface between two isotropic elastic media, within the zeroth approximation of the ray method. Expanding the incident, reflected, and refracted fields near their wave fronts and…
The paper derives a particular solution of the general equations of ideal plasticity in cylindrical coordinates under the Mises yield condition. Assuming axial symmetry, prescribed radial temperature dependence, temperature dependent expansion and yield limit, selected body forces, and a specified f…
This note classifies nonstationary plane adiabatic flows of a polytropic gas whose characteristics are rectilinear, interpreted as common level lines of the velocity components and sound speed in space-time. The Euler and continuity equations are transformed to characteristic parameters, producing a…
This paper studies an axisymmetric plane strain problem for a medium outside an expanding and rotating circular cavity, where small stresses are elastic and larger stresses produce friable behavior. The analysis formulates the stress, displacement, and moving boundary between elastic and friable zon…
The paper studies one-degree-of-freedom oscillatory systems whose mass, restoring force, perturbation, and parameters vary slowly and may depend on the oscillatory state. Using an asymptotic averaging approach over times of order 1/epsilon, it derives equations for the extrema of the coordinate, the…
This paper studies the nonlinear boundary value problem arising in the longitudinal bending of a rod with variable stiffness, reformulated as a nonlinear integral equation for the curvature. Using methods developed by Uryson, it constructs positive solutions by successive approximations from a suita…
This paper studies the torsion of an infinite cylindrical shaft with a circular annular groove, focusing on the determination of maximum shear stresses where exact solutions are unavailable. Using the method of majorant domains, it constructs upper and lower bounds for the stress vector and derives …
This paper examines how the length to diameter ratio of a heated vertical tube affects critical heat flux during forced flow of steam, water mixtures and subcooled water. Experiments were performed in 3 mm stainless steel tubes of 150 and 35 mm length at pressures of 26 and 180 ata, mass velocities …
The paper develops a moment formulation of the Boltzmann equation intended for rapid gas-dynamic processes, without imposing restrictions on the ratio of molecular relaxation time to the characteristic time of the process. Expanding the single-particle distribution function in generalized Hermite po…
The paper analyzes plane outflow from a vessel whose walls form a small angle, with emphasis on the shape and contraction of the emerging jet. Using Chaplygin’s formulation in terms of velocity potential and stream function, together with asymptotic expansions of Chaplygin’s auxiliary function due t…
The paper analyzes heat transfer in the boundary layer on a rotating disk, comparing the turbulent tangential momentum equation with the energy equation for an incompressible fluid. It shows that for a quadratic wall-temperature distribution and unit Prandtl number, the temperature and tangential-ve…
The paper analyzes the axial compression stability of a hollow cylindrical shell using the mathematical theory of elasticity, following nonlinear elasticity ideas while neglecting rotation components in the equilibrium equations but retaining the deformation of the boundary surface. For an axisymmet…
This paper studies axisymmetric supersonic gas flow past a body of revolution using the characteristic form of the governing equations. It derives an evolution equation along characteristics for the derivative of the Mach angle function and relates its boundary condition to the radius of curvature o…
This paper studies the steady flow of an ideal incompressible heavy fluid of finite depth past a submerged hydrofoil, formulated as a nonlinear free boundary problem with a free surface and bottom boundary. Using an inverse method, the physical flow domain is conformally mapped to a strip, the hydro…
The paper analyzes local stresses in a circular prismatic bar subjected to transverse bending and weakened by an eccentric longitudinal elliptical cavity. Using complex-variable methods in elasticity, the elliptical boundary is mapped to a circle, boundary conditions are transformed into functional …
The paper analyzes the onset and development of small two-dimensional oscillations in the viscous wake behind a body using the Orr-Sommerfeld stability equation with a Tollmien-type wake velocity profile. After nondimensionalization, the stability problem is solved approximately by the Galerkin meth…
The paper develops an averaging procedure for canonical Hamiltonian systems containing an angular coordinate whose conjugate momentum varies only by terms proportional to a small parameter, described as a quasi-cyclic coordinate. Using a Krylov-Bogolyubov style first approximation, the generalized c…
This paper examines nonuniqueness in the nonlinear plane hydrofoil problem for flows with a free surface, especially for Froude numbers near the critical value. Using a conformal mapping formulation and Lavrent’ev-type estimates for the free boundary, the authors derive an approximate nonlinear diff…
This paper formulates an exact similarity reduction for unsteady axisymmetric motion of a viscous incompressible fluid between two parallel rotating disks with time-dependent angular velocities and injection velocities. The Navier-Stokes equations are reduced to a coupled system of one-dimensional n…
This paper formulates a linearized boundary value problem for a thin finite span wing with a symmetric profile, zero angle of attack, and arbitrary planform moving in an unbounded compressible fluid. The analysis allows rectilinear translational motion with variable velocity and small symmetric unst…
This paper reports an experimental study of the boundary of the elastic state in thin walled nickel tubes plastically prestrained in tension and then subjected to combined tension and torsion. Using carefully controlled loading, deformation measurements, varied holding times, and specified tolerance…
This paper treats the diffraction of a plane longitudinal elastic wave by a reentrant angle in an elastic medium under boundary conditions of zero tangential stress and zero normal displacement, corresponding mechanically to adhesion without friction. The authors argue that these conditions allow th…
This paper applies the ray method in elasticity to determine the intensity and form of head waves generated when a linearly polarized wave with an arbitrary front is incident on a plane interface between two elastic half-spaces. Using asymptotic expansions of displacement fields, boundary continuity…
This paper examines the limits of Euler linearization in stability problems for elastic shells using the nonlinear theory of shells under Mushtari-type simplifications. For a clamped shell, the nonlinear boundary-value problem is compared with its linearized eigenvalue problem, and several theorems …
This paper extends Sedov’s exact solutions for one-dimensional unsteady motion of an ideal nonconducting gas, in which velocity is linear in distance, by matching them to shock and detonation waves propagating into a gas initially at rest with constant pressure and variable density. Using the jump c…
The paper examines whether an ideal, nonconducting gas can contain a shock wave followed by a region where sound speed is nonzero but disturbances, including another shock wave, never overtake the leading shock. It constructs exact limiting self-similar solutions of the one-dimensional unsteady gas-…
The paper studies the free motion of a balanced gyroscope in a gimbal suspension on a fixed base when dry friction acts in the suspension axes and is proportional to the dynamic reactions. Equations of motion are formulated for the outer ring, inner ring, and rotor, then simplified for small angles …
The paper studies the unsteady motion of a gas driven by an expanding piston as a model for the displacement of air by explosion products, allowing for a nonzero initial pressure. It formulates the resulting non-self-similar problem in dimensionless variables and develops a linearized expansion abou…
The paper analyzes the stability of a thin orthotropic cylindrical shell of medium length subjected to torsion in the presence of internal pressure, extending earlier results for isotropic shells. Starting from shell equilibrium equations with orthotropic elastic constants, the authors derive a Donn…
This paper analyzes filtration in a porous medium when a two-component mixture is displaced by a third immiscible liquid, with special attention to the case where one displaced component has much lower viscosity than the others, as in gas-oil systems under water flooding. Using continuity equations …
The paper formulates a thermodynamic equilibrium condition for gas motions containing surfaces of strong discontinuity, supplementing variational principles for hydrodynamic motion with a variational form of the second law. Using the conservation laws across a shock, detonation, or reaction front an…
This paper examines scattering of sound waves by irregularities in a rectangular waveguide, extending earlier small perturbation treatments to cases where the scattered field need not be small relative to the incident field. Using a modified Rytov method applied to normal wave propagation, it derive…
The paper extends Chaplygin’s equation for steady gas flow by identifying an additional separable family of particular solutions for the stream function. It analyzes the associated differential equation, transforms it to a spectral form, and derives inversion formulas using asymptotic series for two…
This paper addresses the calculation of axisymmetric potential motions of a fluid in a circular pipeline containing bodies symmetric about the pipe axis, a problem for which general exact analytic solutions were not available. Two approximate approaches are proposed: an expansion of the velocity pot…
This paper develops structural and geometric relations for closed complex kinematic chains. It defines independent simple closed contours, derives formulas for their number in terms of link multiplicities and numbers of pairs, and formulates transformation equations whose rank is treated as an intri…
The paper studies mathematical questions in the dynamic stability of elastic systems with periodic perturbations, focusing on second order systems with a positive definite unperturbed matrix and a one-parameter periodic perturbation. It defines resonance and critical frequencies in classes of pertur…
This paper extends a Maxwell-type constitutive law for condensed, practically homogeneous and isotropic bodies from small deformations to cases involving large residual deformation while retaining small elastic strains. It derives tensor relations between stress and strain-rate tensors, allowing the…
This paper studies canonical Hamiltonian systems with quadratic Hamiltonians whose coefficients are periodic functions of a rapidly varying argument, a setting motivated by problems in mechanics such as gyroscope theory. Building on prior reducibility results for the associated linear system, it pro…
This paper studies Riemann waves in ideal magnetohydrodynamics for an arbitrary orientation of the magnetic field relative to a plane wave front, extending earlier treatments restricted to parallel fields. Starting from the isentropic equations for a perfectly conducting gas, it derives characterist…
This paper analyzes the dynamic stability and snap-through of thin cylindrical shell panels with initial imperfections under rapidly applied compressive loading along the generatrix. Using large-deflection shell equations with transverse inertia, a sinusoidal approximation for the deflected surface,…
This paper formulates a class of self-similar solutions for dynamic bending problems of plates governed by the general plate bending equation with moments depending on curvatures. By introducing similarity variables proportional to spatial coordinates divided by the square root of time, the governin…
This paper analyzes the accuracy and convergence of direct variational methods for boundary value problems arising in the nonlinear theory of large shell deformations. It treats the Papkovich and Mushtari approaches by reducing the governing equations to compact operator equations in suitable energy…
The paper examines purely plastic loss of stability in elastic-plastic inhomogeneous shells, with a bimetallic shell used to formulate the stiffness relations. Using Kirchhoff-Love assumptions and allowing for material compressibility, it derives incremental force, moment, strain, and curvature rela…
This paper develops an approximate analytical representation for plane supersonic flows of a compressible gas by replacing the exact coefficient in the characteristic equations with a rational form that permits Darboux-type integration. For adiabatic flow, the approximation is specialized for common…
This paper formulates a plane finite-deformation problem for an incompressible isotropic material using logarithmic principal elongations, rotation, and generalized stresses. It derives compatibility relations for displacements and rotations, introduces a stress function to satisfy equilibrium witho…
This paper derives integral invariants for homogeneous turbulence in a compressible viscous fluid using the conservation laws of momentum, mass, and energy and assumptions on the decay of two-point correlations at large separation. For isotropic turbulence, four nonzero invariants are identified, co…
This paper examines the evaporation of solid volatile spheres in a gas flow, addressing disagreements over whether and how strongly evaporation occurs on the rear side of a sphere. Experiments with naphthalene and camphor spheres used timed photography and weighing to track changes in shape and mass…
The paper analyzes pure torsion of a circular prismatic bar weakened by a longitudinal elliptical hole whose axis is eccentric relative to the bar axis. Using complex-variable elasticity, conformal mapping of the ellipse exterior to a circle, and Sherman’s method, the boundary-value problem is reduc…
