Showing 50 of 813 papers in Mechanics

Toward a Nonlinear Theory of the Onset of Turbulence

E. M. Khazen
1963 SovietRxiv: ru-196301.80889

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…

On the lower critical load for cylindrical shells

Thus, for example, for the lower critical load under axial compression of a cylindrical shell, the formula
1963 SovietRxiv: ru-196301.79861

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…

GAS MOTION BEHIND AN ASYMMETRIC PISTON

Let us consider the motion of a piston that moves according to the law
1963 SovietRxiv: ru-196301.78901

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…

General Forms of Relations Between Tensor Fields in an Anisotropic Continuum Whose Properties Are Described by Vectors, Second-Rank Tensors, and Antisymmetric Third-Rank Tensors

Unknown
1963 SovietRxiv: ru-196301.72685

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…

On the Flow of a Nonequilibrium Gas

V. N. Zhigulev
1963 SovietRxiv: ru-196301.68813

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…

Influence of Changes in the Parameters of Linear Gyroscopic Systems on Oscillation Frequencies and Damping Coefficients

Unknown
1963 SovietRxiv: ru-196301.67950

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…

Finite-Amplitude Shear Waves in Polycrystals and Single Crystals of Metals

A. A. GEDROITS, L. K. ZAREMBO, V. A. KRASIL’NIKOV
1963 SovietRxiv: ru-196301.67375

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…

On Instability Criteria for Shear Deformation Regimes in Viscoelastic Polymer Systems

A. Ya. MALKIN, A. I. LEONOV
1963 SovietRxiv: ru-196301.66583

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…

On the Influence of the Physicochemical Properties of Trapped Gases on the Impregnation of Porous Bodies

Corresponding Member of the Academy of Sciences of the USSR B. V. DERYAGIN, M. A. AL’TSHULER
1963 SovietRxiv: ru-196301.64381

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…

A Case of Integrability of the Equations of Motion of a Heavy Rigid Body with Cavities Filled with Fluid

P. V. Kharlamov
1963 SovietRxiv: ru-196301.62661

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…

Optimal Modes of Motion of a Variable-Mass Point in a Homogeneous Central Field

G. E. KUZMAK, V. K. ISAEV, B. Kh. DAVIDSON
1963 SovietRxiv: ru-196301.61227

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…

ON THE NATURE OF THE CONTACT OF THE FREE SURFACE OF A LIQUID WITH A SOLID BOUNDARY IN THE PROBLEM OF WEDGE PENETRATION

Unknown
1963 SovietRxiv: ru-196301.60108

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…

On the Vibrations of Elastic Rods

I. M. RAPOPORT
1963 SovietRxiv: ru-196301.55286

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…

Toward a Nonlinear Theory of the Development of Aerodynamic Disturbances

Corresponding Member of the Academy of Sciences of the USSR V. V. STRUMINSKII
1963 SovietRxiv: ru-196301.41722

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…

On Some Studies of Spin Detonation

A. A. BORISOV, S. M. KOGARKO
1963 SovietRxiv: ru-196301.41278

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…

Method for Calculating Rarefied Gas Flows

B. V. Kuksenko
1963 SovietRxiv: ru-196301.38789

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…

On the three-dimensional problem of diffraction by a prism

Unknown
1963 SovietRxiv: ru-196301.36766

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. …

Asymptotics of Some Rotational Motions

Unknown
1963 SovietRxiv: ru-196301.36642

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,…

AN ASYMPTOTIC METHOD FOR INVESTIGATING TRANSIENT PROCESSES IN NONLINEAR OSCILLATORY SYSTEMS

We consider a system of nonlinear differential equations
1963 SovietRxiv: ru-196301.34078

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…

Plasticity Bands under Tension of Plates with a Crack-Like Stress Concentrator

Academician of the Academy of Sciences of the Kirghiz SSR M. Ya. LEONOV, P. M. VITVITSKII, S. Ya. YAREMA
1963 SovietRxiv: ru-196301.33953

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…

On the Linear Theory of Sandwich Shells with a Rigid Core

Unknown
1963 SovietRxiv: ru-196301.28239

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…

Method of Integral Moment Kinetic Equations

R. G. BARANTSEV
1963 SovietRxiv: ru-196301.28025

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…

DETERMINATION OF THE SHAPE AND PARAMETERS OF THE FRONT OF A SHOCK WAVE IN AN EXPLOSION IN AN INHOMOGENEOUS MEDIUM

Unknown
1963 SovietRxiv: ru-196301.26992

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…

On Two Gluing Problems

Unknown
1963 SovietRxiv: ru-196301.26454

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…

Toward a Nonlinear Theory of Aerodynamic Stability

Corresponding Member of the Academy of Sciences of the USSR V. V. Struminskii
1963 SovietRxiv: ru-196301.23475

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…

Two-Dimensional Problem of Elastic Collision of Rods

Unknown
1963 SovietRxiv: ru-196301.23162

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,…

Buckling of a shell of revolution under external pressure uniformly distributed along a parallel

Corresponding Member of the Academy of Sciences of the USSR A. V. POGORELOV
1963 SovietRxiv: ru-196301.22886

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…

Some Problems of Cylindrical Bending of Three-Layer Plates Considering Highly Elastic Deformation of the Fiberglass Face Sheet

Unknown
1963 SovietRxiv: ru-196301.21634

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…

Three-dimensional homogeneous expansion–compression of a rarefied gas with power-law interaction functions

A. A. Nikolsky
1963 SovietRxiv: ru-196301.14353

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…

Cruciform Wing of Finite Span in Compressible Flow

Unknown
1963 SovietRxiv: ru-196301.07633

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…

On the Stability of Shaft Motion

Yu. V. OSETINSKII
1963 SovietRxiv: ru-196301.06422

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…

On the system of Prandtl equations in boundary layer theory

In this paper we study the system of boundary-layer equations for an incompressible fluid
1963 SovietRxiv: ru-196301.05849

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…

A Numerical Method for Calculating the Propagation of Long Waves in Open Channels and Its Application to the Flood Problem

O. F. Vasiliev, S. K. Godunov, N. A. Pritvits, T. A. Temnoeva, I. L. Fryazinova, S. M. Shugrin
1963 SovietRxiv: ru-196301.01494

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…

Formation of a Front Stagnant Zone in the Flow of a Viscoplastic Fluid Around Blunt Bodies

I. G. BULINA and V. G. SAVIN
1962 SovietRxiv: ru-196201.98246

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…