Showing 50 of 813 papers in Mechanics

On the Stability of Equilibrium of Systems with Infinitely Many Degrees of Freedom in the Sense of Lyapunov

A. M. SLOBODKIN
1964 SovietRxiv: ru-196401.57852

This paper examines Lyapunov stability for equilibria of mechanical systems with infinitely many degrees of freedom, emphasizing differences from finite-dimensional systems. Using explicit solution formulas for a fixed string, a fixed rectangular membrane, and a clamped elastic parallelepiped, it sh…

On the Refinement of the Plane Reflection Hypothesis

Unknown
1964 SovietRxiv: ru-196401.56282

This note refines the plane reflection hypothesis used to approximate the interaction of acoustic waves with elastic bodies, particularly when exact solutions are computationally difficult. Using orthogonal curvilinear coordinates tied to a body surface, the authors reduce the acoustic wave equation…

On the Question of Creep under Pulsating Stress

I. A. ODING
1964 SovietRxiv: ru-196401.55123

The paper examines high temperature creep under pulsating and changing stress using a rheological model composed of two elastic and two viscous elements whose properties may depend on stress. It proposes a graphical method for constructing deformation over time under periodic unloading and reloading…

On the Rate of Physicochemical Transformations of $\mathrm{CO}_2$ Molecules Behind a Shock Wave at Temperatures of 2000–4000 $^\circ$ K

T. V. Bazhenova, I. M. Naboko
1964 SovietRxiv: ru-196401.53217

This study examines the rate of vibrational excitation and dissociation of carbon dioxide molecules behind shock waves at temperatures corresponding to Mach numbers 6 to 11. The authors compare calculated flow parameters for different nonequilibrium states with shock tube measurements obtained by To…

Generalized Analogy Between Mass Transfer Coefficients in a Laminar Multicomponent Boundary Layer with an Arbitrary Pressure Gradient

Unknown
1964 SovietRxiv: ru-196401.49268

This paper extends a generalized analogy for mass transfer in a laminar multicomponent boundary layer to flows with arbitrary longitudinal pressure gradient and arbitrary surface blowing distribution, in the absence of homogeneous reactions. Using effective diffusion coefficients, Dorodnitsyn-Stepan…

Plane Blast Waves in an Elastic-Plastic Medium

N. V. ZVOLINSKII
1964 SovietRxiv: ru-196401.43709

The paper develops a simplified model for one-dimensional plane explosive waves in an elastoplastic medium whose volumetric and shear response is piecewise linear and may pass through elastic, plastic, and unloading regimes. It classifies four possible medium types according to the sequence of stres…

On the Causes of Shock Wave Formation in Laval Nozzles

Yu. B. Lifshits, O. S. Ryzhov
1964 SovietRxiv: ru-196401.42682

This paper investigates why shock waves form near the throat of Laval nozzles in transonic gas flow. It studies a self-similar class of discontinuous solutions of the transonic flow equations with power-law Cauchy data on the symmetry axis, reduces the governing problem to an ordinary differential e…

Transverse bending of an isotropic plane supported by a doubly periodic system of point supports

È. I. Grigolyuk, L. A. Fil'shtinskii
1964 SovietRxiv: ru-196401.42659

The paper studies transverse bending of an isotropic elastic plate on a doubly periodic lattice of point supports under a uniform transverse load, with attention to stress behavior near the supports. Using complex-variable representations of the biharmonic plate equation, the authors construct doubl…

Dislocation Theorem

M. Ya. Leonov, K. N. Rusinko
1964 SovietRxiv: ru-196401.38849

This paper studies brittle fracture in an unbounded elastic body containing an inserted or removed material half-plane and subjected to uniform tension perpendicular to it. Using a crack model in which the faces interact through a continuous nonincreasing separation stress, the authors formulate an …

On Oscillations of a Viscous Fluid in a Vessel

Unknown
1964 SovietRxiv: ru-196401.37869

The paper studies small motions of a heavy viscous incompressible liquid in an open vessel with a free surface, neglecting surface tension, after linearization of the Navier-Stokes equations. Using variational formulations in a Sobolev space of solenoidal velocity fields, auxiliary boundary value pr…

Impulse pressures in the zone of a secondary erosion focus

Unknown
1964 SovietRxiv: ru-196401.36808

This paper investigates pressure pulsations associated with secondary cavitation erosion foci formed downstream of a circular-profile model in bounded flow. Piezoelectric pickups mounted flush with the wall in the secondary erosion zone were used to record pressure pulses and spectra for several flo…

Application of the diffraction shadow method for quantitative determination of the strength of a plane shock wave near a model in a supersonic flow

Unknown
1964 SovietRxiv: ru-196401.32262

This paper examines the use of the diffraction shadow method for quantitatively determining the intensity of plane shock waves formed at a model in a supersonic flow. The authors derive and analyze formulas relating photographic density in diffraction maxima to optical path difference, including est…

New particular solutions of the problem of the motion of a heavy rigid body about a fixed point

Yu. A. ARKHANGELSKII
1964 SovietRxiv: ru-196401.30810

This paper studies particular periodic solutions of the Euler-Poisson equations for the motion of a heavy rigid body about a fixed point, in the limiting case where the initial rotation about a principal inertia axis is large and the parameter satisfies omega equals one half. It derives additional e…

Three-layer rectangular plate in a supersonic gas flow

È. I. Grigolyuk, A. P. Mikhaĭlov
1964 SovietRxiv: ru-196401.29240

This paper analyzes the linear aeroelastic stability of a simply supported rectangular three-layer plate with an asymmetric thickness structure and a rigid core, subjected to in-plane normal and shear forces and exposed on one side to a supersonic gas flow. The formulation incorporates transverse sh…

Investigation of Supersonic Flow Around a Sphere by Air and Carbon Dioxide in Thermochemical Equilibrium

Unknown
1964 SovietRxiv: ru-196401.26947

This paper presents a numerical investigation of supersonic flow past a sphere with a detached shock wave for air and carbon dioxide under thermochemical equilibrium. The authors formulate the transformed governing equations with equilibrium thermodynamic functions, apply shock and body boundary con…

THREE-DIMENSIONAL FLOW PAST BLUNT BODIES WITH ALLOWANCE FOR EQUILIBRIUM PHYSICOCHEMICAL REACTIONS

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1964 SovietRxiv: ru-196401.22976

This paper addresses numerical calculation of high-speed three-dimensional flow past blunt bodies when equilibrium physicochemical reactions in the gas affect the thermodynamic properties. It introduces an effective isentropic exponent as a function of pressure and density and proposes a compact app…

Polymer Rheology. Theory of Thixotropy

Unknown
1964 SovietRxiv: ru-196401.20041

This paper develops a rheological theory of thixotropy in condensed polymer systems, treating thixotropy as a reversible, time-dependent change in structure and properties under mechanical deformation. The authors model a thixotropic viscoelastic medium as parallel Maxwell elements whose structural …

On the Stability of Poiseuille Flow in a Plane Channel

Unknown
1964 SovietRxiv: ru-196401.19233

This note gives a rigorous proof of the linear instability of Poiseuille flow in a plane channel by studying the Orr, Sommerfeld eigenvalue problem for complex wave speed. After transforming the problem near a critical point, it constructs smooth inviscid and boundary-layer fundamental solutions, de…

Properties of a Hydrodynamic Flow Around Very Small Stationary Obstacles and the Efficiency of Aerosol Particle Capture

Unknown
1964 SovietRxiv: ru-196401.18289

This paper examines low Mach number gas flow past stationary spherical and cylindrical obstacles whose radii are comparable with the molecular mean free path, where classical no slip hydrodynamic boundary conditions are inadequate. By matching viscous hydrodynamic stresses outside a transition surfa…

Riemannian Waves in Relativistic Magnetohydrodynamics

Unknown
1964 SovietRxiv: ru-196401.14619

The paper analyzes Riemann, or simple, waves in relativistic magnetohydrodynamics for a nonviscous, non-heat-conducting, perfectly conducting medium. Using auxiliary gas variables, it reformulates the relativistic MHD equations for two equations of state and derives the governing relations for one-d…

Hypersonic Flow Around Wings at High Angles of Attack

Unknown
1964 SovietRxiv: ru-196401.13161

This paper develops an approximate treatment of hypersonic flow past plane wings at large angles of attack, using a simplified integral-relations formulation analogous to the shallow-water approximation for the thin compressed layer between the shock and the windward surface. The governing equations…

A kinematic interpretation of one solution of the problem of the motion of a body with a fixed point

Unknown
1964 SovietRxiv: ru-196401.12796

The paper gives a kinematic interpretation of a previously obtained solution for the motion of a rigid body with a fixed point, using dimensionless variables for the angular velocity and direction cosines. It derives the moving and fixed hodographs of the angular velocity, showing that the moving ho…

On the Stability of a Cylindrical Shell Under Longitudinal Impact

V. L. AGAMIROV, A. S. VOL’MIR
1964 SovietRxiv: ru-196401.11363

This paper examines dynamic buckling of a circular cylindrical shell subjected to a central longitudinal impact at its free end, with the opposite end fixed. The authors separate, in first approximation, axial elastic wave propagation from shell buckling, estimate the time dependent mean axial stres…

On the Initial Stage of Plastic Deformation in Polycrystals

Unknown
1964 SovietRxiv: ru-196401.08147

This study investigates the onset and early development of plastic deformation in polycrystalline austenitic steel 1Kh18N9T using thin photoelastic epoxy coatings observed in polarized light. The method allowed local measurement of the magnitude and direction of principal strain differences within i…

Experimental Study of the Stability of Shock Waves and the Mechanical Properties of Matter at High Pressures and Temperatures

Unknown
1964 SovietRxiv: ru-196401.06873

This paper reports an experimental investigation of the stability of plane shock waves in condensed media and compares the development of imposed sinusoidal front perturbations with linear calculations for an ideal fluid. Using profiled disks, wedges, and optical streak recording, the authors measur…

General approximate theory of elastic waves in crystals

F. I. Fedorov
1964 SovietRxiv: ru-196401.06190

This paper develops a general approximate method for determining plane elastic waves in homogeneous crystals, where the exact problem normally requires solving a full cubic characteristic equation for each propagation direction. The method represents the elastic wave tensor as an isotropic part plus…

A SEMI-MOMENTLESS THEORY OF CYLINDRICAL PLASTIC SHELLS

Unknown
1964 SovietRxiv: ru-196401.03931

This paper develops a semi-momentless formulation for determining the thickness and internal forces of orthotropic cylindrical plastic shells under prescribed loading. By neglecting longitudinal bending and twisting moments, the yield condition is expressed in terms of longitudinal force, shear forc…

On the Theory of Quasi-Transverse Elastic Waves in Crystals

Unknown
1963 SovietRxiv: ru-196301.98655

This paper develops an approximate method for determining the velocity and displacement of quasi-transverse elastic waves in an arbitrary crystal. The approach replaces the crystal, for a given propagation direction and chosen symmetry axis, by the closest transversely isotropic medium in a least-sq…

Study of the Spatial Behavior of Composite Structures

B. P. Vol'fson
1963 SovietRxiv: ru-196301.97599

This paper develops a general analytical formulation for the spatial behavior of composite structures made of several connected elements with elastic, compliant joints distributed along their seams. Using assumed displacement functions across the transverse section, Hooke’s law, and Lagrange’s princ…

ON CAPILLARY EQUILIBRIUM IN A MODEL OF A POROUS BODY WITH INTERSECTING PORES OF VARIABLE CROSS SECTION

Unknown
1963 SovietRxiv: ru-196301.96124

This paper analyzes capillary equilibrium and gas penetration in a porous body whose intersecting pores have variable cross section, extending earlier treatments that assumed constant pore radius. The porous structure is modeled probabilistically: supercritical pore branching and pore “death,” where…

On the Basic Equations of the Theory of Elastic Shells

Unknown
1963 SovietRxiv: ru-196301.91246

This paper develops a method for deriving self-adjoint equilibrium equations for thin elastic shells of arbitrary configuration, addressing difficulties in extending earlier Love, Timoshenko, and Vlasov formulations to general shells with body forces. The approach starts from the three-dimensional e…

Periodic Waves Generated by a Source Located Above an Inclined Bottom

Corresponding Member of the Academy of Sciences of the USSR L. N. SRETENSKII
1963 SovietRxiv: ru-196301.89193

This paper studies periodic surface waves generated by a source with harmonically varying discharge located above a uniformly sloping bottom. Under assumptions of plane parallel potential flow and for bottom angles that are integral fractions of a right angle, the problem is reduced to a constant co…

A SHOCK WAVE OF FRACTURE IN BRITTLE MEDIA

Unknown
1963 SovietRxiv: ru-196301.88922

The paper develops a continuum-mechanical model for the formation and propagation of a fracture shock wave produced by an explosion in a brittle medium. Assuming spherical symmetry, it treats the intact material ahead of the front as a linear elastic solid, the crushed material behind it as an incom…

Postcritical deformations of boundedly elastic shells

Corresponding Member of the Academy of Sciences of the USSR A. V. POGORELOV
1963 SovietRxiv: ru-196301.85336

This paper examines postcritical deformation in geometrically nonbendable elastic shells when the material has a finite elastic limit. It argues that loss of stability produces sharp edge-like singularities, and that if bending near such an edge causes plastic deformation, the local surface form bec…

Ship Waves in a Viscous Fluid

L. V. CHERKESOV
1963 SovietRxiv: ru-196301.85260

This note analyzes the three-dimensional wave pattern generated on the free surface of a viscous incompressible fluid by a system of normal stresses moving uniformly along the surface. Using the linearized hydrodynamic equations, free-surface boundary conditions, and Fourier transforms, it derives a…

On the Theory of Complex Media

Unknown
1963 SovietRxiv: ru-196301.81867

This paper develops a framework for constructing stress strain relations for a broad class of complex continuous media built from elastic, viscous, and plastic deformation mechanisms. Using one-dimensional and two-dimensional dynamical models, it introduces an indexing scheme for combinations of mec…