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 nonlinear closure for describing the onset and growth of turbulence in viscous incompressible flow beyond the small fluctuation regime treated by linearized or Gaussian approximations. It proposes a moment hypothesis relating fifth-order central moments to products of second- a…
This note examines lower critical loads for comparatively thick cylindrical shells whose postcritical deformations may produce stresses beyond the elastic limit of a material with limited elasticity. Building on earlier treatments for shells of unlimited elasticity, it argues that the ridge formatio…
The paper analyzes gas motion behind a slightly asymmetric cylindrical or axisymmetric piston moving with constant speed in a gas initially at rest. It reformulates the gas-dynamic equations in coordinates adapted to the piston shape, introduces similarity variables, and treats the asymmetry as a sm…
The paper studies special integrable cases of the equations of motion for a heavy gyrostat fixed at one point, with a flywheel contributing constant angular momentum components in body axes. It first extends the Goryachev-Chaplygin case under the conditions that two flywheel momentum components vani…
This paper examines how mechanically induced particle orientation affects the structural and mechanical properties of aqueous palygorskite pastes. Using rolling to align fibrous mineral particles from the Cherkassy deposit, the authors compare elastic, plastic, and viscous constants for unoriented s…
This paper develops a general representation for nonlinear invariant tensor relations in anisotropic continua whose defining parameters may include vectors, symmetric and antisymmetric second-rank tensors, and antisymmetric third-rank tensors. The argument expresses an arbitrary tensor function thro…
The paper addresses a three-dimensional contact problem in linear elasticity for a finite rectangular parallelepiped placed in a rigid pit and pressed by a rigid punch over a prescribed contact region. Using a Papkovich-Neuber representation, the displacement field is expressed through two harmonic …
The paper examines gas flows with relaxation of low energy internal degrees of freedom or reactions, distinguishing weakly relaxing media from flows close to thermodynamic equilibrium. A small parameter expansion is formulated for weak relaxation and applied to vibrational relaxation, yielding first…
This paper examines how changes in the parameters of linear gyroscopic systems affect characteristic roots, and hence oscillation frequencies and damping coefficients. Starting from the quadratic characteristic equation expressed through mass, damping, gyroscopic, stiffness, and nonconservative-forc…
This paper reports experimental observations of nonlinear distortion in finite amplitude shear ultrasonic waves in polycrystalline metals and metal single crystals, detected through generation of a second harmonic. Using 5 MHz shear waves and resonant detection at 10 MHz, the authors examine magnesi…
This note develops a tangential-coordinate formulation for the general theory of reduced accelerations of arbitrary order in mechanisms undergoing spatial motion. Starting from vector equations for a moving plane and the locus of endpoints of higher-order acceleration vectors, the authors derive par…
The paper examines the onset of unstable shear deformation regimes in elastic-viscous polymer systems, particularly disturbances observed during polymer melt flow through capillaries. Using similarity theory applied first to Maxwell and related viscoelastic deformation models, the authors derive a s…
This paper examines how the solubility and diffusion of gases trapped in blind capillaries or fully immersed porous bodies affect capillary impregnation by liquids. Starting from earlier equations for impregnation with insoluble gases, the authors formulate a coupled description of liquid motion and…
This paper studies the motion of a heavy rigid body with a fixed point and cavities filled with an ideal liquid, including multiply connected cavities with prescribed circulations. Starting from Zhukovskii’s equations and their standard first integrals, it seeks an analogue of the Bobylev-Steklov in…
This paper studies optimal control for the motion of a variable mass point in a homogeneous central gravitational field under bounded reactive thrust. Using Pontryagin’s maximum principle, the authors derive adjoint equations and exploit their explicit solution in the approximating field model, wher…
This paper examines the analogy between hypersonic flow past thin bodies with blunt leading parts and the flow produced by a strong cylindrical explosion. It reviews how the analogy supports similarity laws and integral methods for predicting pressure and drag, including the differing effects of blu…
The paper studies the nonlinear self-similar problem of a wedge penetrating an ideal incompressible weightless liquid at constant velocity, focusing on the previously unresolved contact between the liquid free surface and the solid wedge boundary. The flow is formulated through a conformal mapping f…
The paper develops a method for reducing three-dimensional static and dynamic elasticity problems for rods to one-dimensional form without relying on the plane-section hypothesis. Elastic displacements are expanded in double power series over the cross-section coordinates, leading to an infinite sys…
The paper analyzes the gas motion produced by a short-duration plane impact or explosion in an inhomogeneous atmosphere whose initial density follows a barometric law and whose initial pressure is zero. Using dimensional arguments and Lagrangian gas-dynamic equations, it derives a self-similar formu…
This paper addresses the nonlinear time development of disturbances in laminar viscous incompressible flows, where conventional linear stability theory is valid only for sufficiently small times. It applies a modified small-parameter method analogous to Poincaré’s method, introducing an auxiliary ti…
This paper examines the structure and mechanism of spin detonation, arguing that acoustic theory does not adequately account for observed breaks and terminal disturbances in the shock front. Using smoked-film trace records, ionization probes, and corona-discharge probes in methane-oxygen mixtures, t…
This paper proposes a computational method for rarefied gas aerodynamics that reduces the difficulty of solving integral kinetic equations involving functions of many variables. Using a Hermite polynomial expansion of the distribution function, the author derives nonlinear integral equations for den…
The paper studies the three-dimensional diffraction of waves by an infinite prism with a convex polygonal base, focusing on the Green function for the wave equation with zero boundary conditions and on the singularities that determine high-frequency behavior for the corresponding Helmholtz problem. …
The paper studies rotational regimes in one degree of freedom systems that are small perturbations of Hamiltonian motion with slowly varying parameters and periodic potential forces. Using first approximation averaging methods, it derives equivalent evolution equations for the slowly varying energy,…
This paper develops an asymptotic procedure for studying transient processes in weakly nonlinear oscillatory systems with many degrees of freedom, formulated as a system of second order differential equations with a small parameter and periodic forcing variables. Under assumptions on the characteris…
This paper investigates the initiation and development of localized plasticity bands in thin steel plates containing a crack-like slit and subjected to tensile loading perpendicular to the concentrator. Experiments on normalized and polished mild steel specimens identify successive deformation stage…
This paper develops nonlinear equilibrium equations for shallow three-layer shells of nonsymmetric construction undergoing large deflection. Using Kirchhoff-Love assumptions for the load-bearing layers, a transversely isotropic rigid core with transverse compression neglected, and a linear approxima…
This paper develops general equations for the equilibrium and free vibrations of thin three-layer shells of asymmetric construction with an orthotropic rigid core that may undergo transverse compression. Using the middle surface of the core as the reference surface, the authors assume Kirchhoff Love…
The paper proposes a method for treating kinetic problems in rarefied gas aerodynamics without constructing the full molecular distribution function. It expands the distribution function in generalized Hermite polynomials, whose leading coefficients correspond to principal macroscopic gas characteri…
This note studies the linear stability of Taylor flow, the motion of a viscous incompressible fluid between coaxial rotating cylinders, in the large Reynolds number regime. The eigenvalue problem for viscous perturbations is reduced to a single ordinary differential equation and compared with the li…
An approximate method is developed for determining the front shape and parameters of a shock wave produced by a point explosion in an inhomogeneous ideal medium. The paper formulates the dimensional dependencies, derives a first-order nonlinear equation for the evolving shock front from the normal s…
The paper studies two free-boundary gluing problems for plane hydrodynamic flows in which harmonic and constant-vorticity regions are joined across an unknown curve with continuous first derivatives of the stream function. For the first problem, the gluing curve is characterized by an integral equat…
This paper examines nonlinear aerodynamic stability of laminar viscous incompressible flows, focusing on channel flow and boundary-layer approximations. It applies a small-parameter method in which the first approximation is the usual linear Orr-Sommerfeld problem and higher approximations are obtai…
This paper studies the two-dimensional elastic collision of flat semi-infinite rods, motivated by the reduction of cylindrical rod impact problems to this case. The analysis formulates the motion in terms of volumetric and shear strain functions, applies Sobolev’s method directly to these functions,…
This paper studies the loss of stability of a shell of revolution subjected to normal pressure uniformly distributed along a parallel. The analysis approximates the buckled shape by an isometric double mirror reflection of portions of the original surface, reduces the deformation energy near the aff…
The paper studies the analytic structure of solutions to the nonlinear membrane equation for a circular thin plate under three boundary conditions: prescribed contour tension, absence of shearing forces, and absence of radial contour displacements. For the tension and displacement conditions, the eq…
This paper develops a theory for cylindrical bending of three-layer plates with light cores and fiberglass skins, accounting for reversible high-elastic deformation in the skins in addition to ordinary elastic strain. Using assumptions for a transversely compliant core and Reissner-type facings, the…
This paper examines the stability loss of a thick, freely supported rectangular plate uniformly compressed in one direction, explicitly accounting for rotation angles in the sense of Novozhilov’s stability theory. Using small elastic plastic deformation relations for an incompressible material, the …
This paper examines how static strength changes at stress concentration sites, questioning the usual practice of comparing the maximum local stress directly with the material strength limit. Using cylindrical specimens with grooves of varied depth and curvature, tested in steel 45, quenched and temp…
This paper studies elastic, rigid, plastic torsion of a cylindrical rod with a strictly convex oval cross-section, formulating the problem in terms of a stress function with an unknown elastic core and a surrounding plastic region. Using support-function coordinates for the boundary, it defines a ge…
This paper theoretically examines the transition between thermal self-ignition and ignition in a reacting cylindrical system whose initial temperature is below that of the surroundings. A nonstationary heat-conduction and reaction equation for a zero-order reaction with fixed surface temperature is …
This paper extends the analysis of three-dimensional homogeneous expansion and compression of rarefied monatomic gases and gas mixtures to particles interacting through power-law repulsive or attractive central forces. Using the Boltzmann equation, the similarity properties of collision transformati…
This paper extends Prandtl’s solution for compression of a plastic strip between rigid rough plates to a small deformation, anisotropically hardening rigid plastic material. The authors introduce a linearized yield condition based on a tangent approximation to the moving yield circle and derive the …
This paper analyzes the linearized problem of a thin cruciform wing of finite span undergoing arbitrary harmonic oscillations in a supersonic compressible flow. Using Hadamard’s method and symmetry with fictitious reflected panels, it derives a basic integral formula for the reduced disturbance pote…
The paper develops a linear elastic theory for small deformations, stability, and vibrations of asymmetric three-layer plates with a rigid core. Assuming Kirchhoff-Love behavior in the two load-bearing layers, transverse incompressibility and linear tangential displacements in the transversely isotr…
The paper examines the stability of uniform rotation of a vertical elastic, weightless shaft carrying a centrally mounted thin disk whose transverse principal moments of inertia are slightly unequal. Linearized equations for small translational and angular perturbations are derived using momentum an…
The paper studies the Prandtl boundary-layer equations for an incompressible fluid in a half-strip with prescribed initial velocity, wall suction or injection, and matching to an outer flow satisfying Bernoulli’s law. Using the von Mises transformation, the system is reduced to a degenerate paraboli…
This paper analyzes the motion of a free gyroscope in a Cardan suspension on a moving base while accounting for the masses of the suspension rings. It derives general kinematic relations, kinetic energy expressions, and Lagrange equations without assuming small ring angles, then applies small-deviat…
This paper presents a numerical method for calculating unsteady long wave propagation in open channels, with emphasis on flood routing in river systems. The authors formulate the Saint Venant equations without neglecting inertial terms and develop a modified implicit finite difference scheme in whic…
This paper reports experimental observations of the flow of a viscoplastic clay suspension around blunt bodies, focusing on the formation of a forward stagnant zone not found in comparable flows of ordinary fluids. Bodies of several shapes were drawn through an open trough at controlled speeds, whil…
