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 studies steady finite amplitude waves on the free surface of an ideal incompressible heavy fluid of infinite depth when a periodic pressure distribution is prescribed on the surface. Using conformal mapping and Bernoulli’s condition, the problem is reduced to a nonlinear integral equation…
This paper investigates supersonic unsteady flow past blunt bodies of revolution undergoing small plane angular oscillations. Using a linear expansion in oscillation amplitude, the steady flow and the disturbance fields in phase with angle of attack and angular velocity are computed numerically in s…
This paper describes a gas-cumulative explosive technique for accelerating solid particles to very high velocities for studies of high-velocity impact. It outlines the use of hollow cylindrical explosive charges that generate a cumulative jet of detonation products, gives approximate design conditio…
This paper studies an axisymmetric ideal incompressible flow with a free boundary in the upper half-plane, where the velocity field satisfies a generalized analytic equation, has a prescribed simple pole, is tangent to the boundary, and has constant modulus on the boundary. The problem is reduced by…
This paper formulates elasticity and deformation plasticity relations for homogeneous isotropic solids whose mechanical properties differ in uniaxial compression, uniaxial tension, and torsion, while allowing small elastoplastic strains and temperature dependence. Constitutive laws are proposed for …
The paper addresses the construction of a stationary probability distribution for turbulent flows, where energy dissipation prevents direct use of Gibbsian statistical methods. For an incompressible viscous fluid, the Navier-Stokes equations with weak broadband random forcing are reduced by a Galerk…
This paper develops a class of exact solutions for biharmonic elasticity problems in a semi-strip, motivated by stress analysis in elasticity and thermoelasticity. Instead of extending the solution through the end of the semi-strip, the authors extend it periodically through the longitudinal edges, …
The paper analyzes Reissner’s nonlinear equations for finite, axisymmetric deformation of thin shallow shells of revolution under symmetric loading, introducing a dimensionless formulation with the shell thinness as a natural small parameter. It outlines a Galerkin approximation scheme but argues th…
This paper constructs an invariant transformation for the equations of plane steady motion of an ideal gas, mapping one flow plane to another while preserving the form of the governing momentum and continuity equations. The transformation changes the equation of state through arbitrary parameters, p…
This paper studies supersonic flow of a viscous compressible gas near a wall with a corner or break. The flow domain is divided into regions treated respectively by the full Navier-Stokes equations, inviscid gas equations, and boundary-layer-type equations, with matching conditions imposed on artifi…
This paper derives relations governing stress discontinuity surfaces in three-dimensional ideal rigid-plastic bodies for a general plasticity condition, using continuity of contact stresses, the yield condition, associated flow, and geometrical compatibility of displacement-velocity derivatives. The…
This paper studies stationary and nonstationary Prandtl boundary-layer systems for axisymmetric incompressible flow past bodies of revolution. By applying a Crocco-type change of variables and constructing solutions through the method of lines, it derives a priori estimates for the resulting degener…
The paper examines how molecular transport processes, such as heat or concentration diffusion, are modified in turbulent flows when described in variables closer to a Lagrangian representation. It introduces coordinates based on particle labeling at a reference surface and travel time, derives avera…
This paper examines the large-time asymptotic propagation of a plane strong detonation wave in a gas at rest when the flow behind the front weakens toward a Chapman-Jouguet wave. Using the detonation jump relations and gas-dynamic equations, it expands the velocity, pressure, and density behind a wa…
This paper analyzes the relative motion of small solid particles suspended in a locally homogeneous, isotropic, stationary turbulent flow, under conditions where particle concentration is low, particle size is below the inner turbulence scale, and particle feedback on the gas is neglected. Starting …
The paper studies flexural vibrations of three-layer beams using a reduced sixth-order differential equation for a displacement function that incorporates shear and layer-structure parameters. Harmonic solutions are expressed through the roots of the associated cubic characteristic equation, yieldin…
This paper analyzes transverse vibrations and flutter of an unbounded three-layer elastic plate or strip in a gas flow. Starting from the differential equation for flexural vibrations, the aerodynamic load is derived for potential flow on both sides of the plate, and the coupled problem is reduced t…
This paper formulates differential equations for the filtration of aerated liquid in porous media while accounting for mass transfer of residual water, a factor often treated as constant in earlier models. Under simplifying assumptions including isothermal flow, ideal gas behavior, Henry’s law, negl…
The paper studies one-dimensional axisymmetric unsteady motions of an infinitely conducting, inviscid perfect gas cylinder under magnetic fields and Newtonian gravity, with temperature independent of radius and with nonzero azimuthal velocity. Assuming a Sedov-type linear radial velocity field, it d…
The paper examines statistical and variational methods for calculating the elastic constants of quasi-isotropic polycrystalline aggregates, focusing on the shear modulus of polycrystals composed of cubic crystallites. It shows that the Hashin and Shtrikman bounds, the results of Lifshitz and Rosenzw…
The paper interprets observations of waves at a near-critical liquid vapor interface as gravity waves and examines how critical behavior modifies their propagation. Using linearized hydrodynamics, it derives dispersion relations for gravity waves on the surface of a compressible liquid and at the in…
The paper formulates a variational principle for dynamics in the linear theory of elasticity that is equivalent to the mixed initial boundary value problem, rather than only to a boundary value formulation. It constructs a functional involving displacement, stress, and strain fields together with ti…
The Lauricella method is applied to reduce the boundary value problem of the equilibrium of a part of a cylindrical shell, bounded by a simply connected smooth contour, to integral equations. The components of the displacement vector and the rotation angles of the shell normal are specified on the c…
The paper studies the boundary value problem for the nonlinear system governing strong bending of a thin clamped elastic plate, with unknown in-plane displacements and transverse deflection. It proves existence of a generalized solution for loads in the negative Sobolev space \(W_2^{-2}\), using Gal…
This paper examines constitutive relations between stress and strain in nonlinear viscoelasticity using an operator formulation in Hilbert spaces over a fixed Lagrangian coordinate system. Assuming a sufficiently smooth stress operator expandable in Fréchet series with an invertible linear part, it …
This paper revisits the gas kinetic calculation of thermal slip, or thermal creep, of a gas along a solid wall in the presence of a tangential temperature gradient. Using analytically corrected values for several linearized Boltzmann collision integral moments, it revises a previously derived molecu…
The paper examines thermal slip of a gas along a solid wall in the presence of a tangential temperature gradient, revisiting Maxwell’s classical result in light of the non-equilibrium velocity distribution within the Knudsen layer. It applies the Bhatnagar, Gross, and Krook relaxation approximation …
This paper studies steady plane motion of an ideal incompressible fluid in a reservoir under Coriolis forces, with particular attention to when a through-flow region cannot occupy the whole basin. The authors formulate a free-boundary problem for the stream function in which flowing zones satisfy a …
An approximate method is developed for integrating the Rayleigh equation with cubic velocity nonlinearity for arbitrary values of the parameter governing nonlinearity, a range in which both amplitude and period may vary strongly. The method uses a harmonic change of variables, quarter-cycle averagin…
This paper revisits the theory of diffusiophoretic motion of large volatile droplets in a binary gas mixture, addressing a discrepancy between an earlier thermodynamic result and a previous direct force calculation. The authors solve the coupled convective diffusion and viscous hydrodynamic equation…
This paper derives equations of motion for a machine unit consisting of an engine, ideal variator, and working machine, treating the prescribed time-varying transmission ratio as a nonholonomic constraint. Using Appell’s equations, the authors formulate equivalent differential equations in terms of …
This note develops evolution equations for finite-dimensional probability distributions of the velocity field in incompressible turbulence. Starting from the Navier-Stokes equations and the pressure representation in terms of velocity, it derives equations for n-point characteristic functions and, b…
A spatial contact problem regarding the pressure of a strip punch on an elastic foundation with an elastic modulus $E=E_m z^m$ ($0<m<1$) is solved. Using the method of Fourier integral transforms, the problem is reduced to dual integral equations of trigonometric type. By means of an existing soluti…
This paper studies unsteady long waves generated by initial disturbances in a rotating channel of constant depth, including disturbances relevant to tsunami-type wave formation. Using Laplace and Fourier transforms, the governing linear hydrodynamic equations are reduced to an inhomogeneous Helmholt…
This paper investigates the mechanism by which a jet in a fluidic amplifier attaches to a diffuser wall, the Coanda effect, with emphasis on the role of pressure pockets and vortex motion. Experiments were conducted in water using a symmetric jet amplifier model with a splitter, high Reynolds number…
The paper examines the role of the dissipative function in the mathematical theory of plastic media and its relation to the conventional formulation based on a loading function and associated flow law. Starting from the Mises maximum principle for hardening plastic bodies, it shows that a first degr…
This paper studies rectilinear stationary motions of an incompressible viscoplastic medium using a variational formulation rather than local differential equations with unknown plastic flow boundaries. For pipe flow under a pressure gradient, the minimization functional is used to establish existenc…
The differential equation $$\ddot{x}+a\dot{x}+f(x)=-u_0\operatorname{sign}(\dot{x}-\varphi(x)),$$ is considered, where $a>0$; $u_0>0$; $f(x)$ and $\varphi(x)$ are periodic and everywhere continuously differentiable functions that vanish at $x=0$ and $x=+\pi$. This equation describes, in particular, …
The article considers a system of fourth-order differential equations describing, in particular, the motion of coupled Froude pendulums of equal masses suspended on a shaft rotating at a speed $\Omega$. The paper provides upper and lower bounds for the values of the speed $\Omega$ in the case of the…
The paper studies the spatial Cauchy-Poisson problem for small long waves on the free surface of a viscous liquid of finite depth, with prescribed initial surface displacement and surface pressure. After linearizing the Navier-Stokes equations, the authors apply Fourier transforms in the horizontal …
This paper examines the use of a diffraction grating interferometer for quantitative investigation of gas flows around models in a shock tube, where simultaneous visualization of shock structures and density measurements is required under vibration and transient conditions. The authors analyze pract…
This paper addresses the experimental study of the transition from linear to nonlinear behavior in parametric resonance for systems approximated by Hill-type equations with periodic coefficients. Using Floquet theory, it derives a relation among three values of a solution separated by one period, al…
This paper considers dynamic synthesis of a mechanical system with a variator, seeking laws of variation of the transmission ratio that realize prescribed motion of either the driving or driven link. Starting from differential equations of motion in relative variables, it derives finite solutions fo…
The paper analyzes the flow produced by a plane, cylindrical, or spherical point explosion in a perfect gas capable of detonating, treating the shock and reaction zone as a single strong discontinuity with heat release. It argues that the early motion is close to the classical point explosion while …
This paper derives explicit half-space potentials for the homogeneous linear system governing small oscillations of a rotating incompressible fluid. Using Laplace transforms in time and Fourier transforms in the tangential spatial variables, it obtains integral formulas for two boundary-value proble…
