Recent Papers

ON STABILIZATION OF DYNAMIC SYSTEMS BY SUPPLEMENTARY FORCES[^1]

PARAMETRIC RESONANCE OF ELASTIC SYSTEMS WITH DISTRIBUTED PARAMETERS

The paper studies parametric resonance and dynamic instability for Hamiltonian equations in a separable Hilbert space, modeling elastic systems with distributed parameters under periodic perturbations. Using a reduction to spectral properties of associated operators, it derives a first approximation…

On rheological relations during the motion of a viscoelastic medium in a field of constant longitudinal velocity gradient

This paper analyzes the motion of incompressible elastic-viscous and thixotropic elastic-viscous media in a field with a constant longitudinal velocity gradient, motivated by stretching processes in fiber and film formation. Using rheological equations satisfying Oldroyd’s space-time invariance prin…

The integral operator method in the hereditary theory of creep

The paper develops an integral operator approach for hereditary creep problems using Volterra operators with Rabotnov type kernels. It reviews known algebraic and differentiation properties of these operators and proves, by induction, a formula expressing products of arbitrary powers of operators wi…

Loss of Stability of Shells of Revolution under Torsion

This paper analyzes the torsional loss of stability of a strictly convex shell of revolution subjected to a moment produced by uniformly distributed tangential edge forces. Using a postcritical approximation in which the deformation is treated as nearly isometric and the elastic energy is concentrat…

On the Influence of Viscosity on the Mechanical Behavior of Plastic Media

This paper examines how internal viscosity affects the mechanical behavior of anisotropically hardening plastic media. It generalizes an elastic-plastic hardening model by adding a viscous element that governs relaxation of residual microstresses, formulates the corresponding yield condition and ass…

THEORY OF SHALLOW ANISOTROPIC PLASTIC SHELLS

A rigid-plastic theory is formulated for shallow orthotropic shells to estimate load-carrying capacity and to identify rational, minimum-weight forms. Using standard shallow-shell equilibrium and kinematic relations together with an anisotropic yield condition and associated flow law, the paper deri…

On the Formulation of the Problem of Shell Buckling under Creep

The paper formulates the buckling problem for shallow shells under creep as the time development of prescribed initial imperfections in a geometrically nonlinear setting. Assuming that stresses and strains during creep remain close to a basic momentless state, the author linearizes the creep relatio…

On the Problem of Optimal Control of a Mathematical Pendulum

Some plane problems of thermoelasticity under periodic thermal actions

This note treats quasistatic plane thermoelasticity problems for plates and cylinders subjected to periodic thermal actions, neglecting coupling between elasticity and heat conduction. Using Bessel-function representations of the periodic heat-conduction problem, it derives thermoelastic displacemen…

TORSION OF COMPOSITE ANISOTROPIC CYLINDRICAL BODIES WITH A SLIGHTLY CURVED AXIS

The paper studies Saint-Venant torsion of composite anisotropic cylindrical bodies with cavities and a slightly curved axis, assuming each material has one plane of elastic symmetry perpendicular to the cylinder axis. By introducing a perturbative coordinate transformation that straightens the axis …

ON THE STABILITY OF PARALLEL FLOWS OF NON-NEWTONIAN MEDIA

On the Shear Elasticity of Boundary Layers of Liquids

This paper investigates the shear elasticity of thin liquid films at solid boundaries, a property relevant to the mechanical behavior of boundary layers and boundary friction. An ultrasonic method using an X-cut piezoquartz resonator was applied to liquid films of controlled thickness between quartz…

On the transition through the speed of sound in Laval nozzles with a circular cross section

This paper studies axisymmetric transonic flow through the speed of sound in circular Laval nozzles, using von Kármán’s equations with prescribed power-law velocity behavior on the nozzle axis. By reducing the self-similar Cauchy problem to an ordinary differential equation in a phase plane, the aut…

Process of Establishing a Steady-State Melting Regime of a Viscous Glassy Material

The paper examines the nonstationary establishment of a steady melting and mass removal regime for viscous glasslike materials, such as quartz glass, exposed to high temperature gas flow near a stagnation point. Using numerical calculations over varied thermophysical parameters and flow conditions, …

An Example of Heteroparametric Excitation of a Pendulum by Quasiperiodic Oscillations of the Suspension

This paper examines heteroparametric excitation of a mathematical pendulum with a vertical axis of rotation when the suspension point undergoes quasiperiodic linear oscillations. Starting from the pendulum equation with viscous damping, the analysis transforms to a uniformly rotating reference frame…

DIFFRACTION OF A PLANE LONGITUDINAL WAVE BY A CIRCULAR CYLINDER

The paper studies diffraction of a stationary plane longitudinal elastic wave by a stress-free circular cylindrical cavity in the high-frequency case where the longitudinal and transverse wave numbers times the cylinder radius are large. Starting from the standard series solution for longitudinal an…

ON THE SOLVABILITY OF FILTRATION PROBLEMS WITH FREE BOUNDARIES

The paper proposes a method for proving existence and constructing solutions to free-boundary filtration problems in earth dams, including cases with infiltration or evaporation on the free surface and seepage face. By transforming the Cauchy-Riemann equations and boundary conditions into a linear e…

On High-Frequency Pulsations during Solid Propellant Combustion

This paper examines high-frequency pulsations during the combustion of solid fuel in a cylindrical grain cavity, focusing on the coupling between acoustic oscillations in the gas and elastic surface waves in the solid propellant. It develops frequency-matching conditions for gas acoustic modes and s…

Relaxation of the vibrational energy of air molecules behind the front of a direct shock wave

This paper examines vibrational energy relaxation of nitrogen and oxygen molecules behind a normal shock wave in air, focusing on when exchange of vibrational quanta between components becomes significant. Treating air as a binary diatomic mixture, the authors couple conservation equations for the n…

A METHOD FOR CALCULATING A POINT EXPLOSION IN GASES

A numerical method is developed for calculating the propagation of blast waves from a point explosion in an inviscid perfect gas with counterpressure, for plane, cylindrical, and spherical symmetry and for various adiabatic exponents. The approach combines central asymptotic formulas with the method…

A wing of finite span in the presence of a moving shock wave

This paper studies the linearized unsteady three dimensional flow of a compressible fluid around a thin finite span wing moving supersonically while encountering a weak plane shock wave inclined to the plane of motion. The velocity potential is decomposed into the potential of the moving shock and a…

On the Problem of the Interaction of Bodies at Very High Velocities

This paper proposes an approximate hydrodynamic model for the high velocity normal impact of a small projectile on a semi-infinite metallic target, in the regime where both materials behind shock waves behave approximately as liquids. The interaction is represented by a mushroom-like projectile form…

On the calculation of creep of beams in bending

This paper presents a method for calculating creep in beams under pure bending using a four-element elastic-viscous phenomenological model whose parameters depend on stress. To make the nonlinear problem tractable, the stress-dependent elastic and viscous characteristics are approximated as piecewis…

THE SECOND BOUNDARY-VALUE PROBLEM OF THE THEORY OF ELASTICITY FOR A HOMOGENEOUS ISOTROPIC LAYER

The paper treats the displacement boundary-value problem for the Lamé system in a homogeneous isotropic elastic layer with prescribed displacements on the two bounding planes. Using invariance under the group of plane-parallel motions, the solution is expanded in minimal invariant subspaces expresse…

Load Transfer from a Finite-Length Stringer to an Infinite and Semi-Infinite Plate

The paper studies the transfer of an axial end load from a finite riveted stringer to an infinite or semi-infinite elastic plate, seeking the distributed load transmitted along the attachment segment. Using known plane elasticity solutions for concentrated forces, the compatibility of stringer and p…

Loss of Stability of a Convex Shell under the Pressure of a Taut Thread

This note examines the loss of stability of a strictly convex elastic shell, fixed along its boundary, under the pressure exerted by a taut string. Using the mirror bulging approximation for the postcritical deformation, it compares the elastic deformation energy of the shell with the work done by t…

On Hilbert’s Method for Solving the Boltzmann Kinetic Equation

This paper examines the applicability of Hilbert’s small-parameter method for solving the kinetic Boltzmann equation and its relation to hydrodynamic approximations. By analyzing the recurrent integral equations and their solvability conditions, it argues that Hilbert’s general formulation yields a …

Buckling of Shells of Revolution Under Internal Pressure

This note investigates the loss of stability of convex shells of revolution under internal pressure, focusing on the formation of localized bulges arranged along a parallel. Using a geometrical approach, it models the deformation energy as concentrated near the boundaries of small elliptical bulging…

Mechanisms for Reproducing Parabolic and Hyperbolic Curves

The paper develops the kinematic theory of three related six-link mechanisms for generating algebraic curves of parabolic and hyperbolic type. Using geometric relations among sliders, levers, and fixed guides, it derives equations for the paths traced by selected mechanism points, including third-or…

On the generalization of the method for solving axisymmetric problems in elasticity theory using analytic functions to spatial problems without axial symmetry

On a Particular Solution of the Equations of the Theory of Ideal Plasticity

This paper derives a particular three-dimensional solution of the equations of ideal plastic flow under the Huber-Mises yield condition in Cartesian coordinates. By assuming that selected components of the strain-rate tensor are independent of two spatial coordinates and that a shear stress componen…

ON CERTAIN FEATURES OF THE MECHANICAL DESTRUCTION OF ROCKS UNDER THE ACTION OF STATIC, IMPACT, AND PULSATING LOADS

This paper examines how quartzite specimens fracture under static, impact, and pulsating loads applied through a spherical contact, as a model for rock crushing between machine surfaces. Using petrographic thin sections and microscopic examination of fractured and indented specimens, the study compa…

Statistical Description of the Stress State of a Deformable Body

This paper formulates a statistical description of the stress state of a deformable body when the stress tensor is treated as a random tensor field, arising for example from random external forces or statistically specified microinhomogeneity. It defines multipoint probability densities and tensor m…

A New Solution to the Problem of Motion in a Newtonian Force Field of a Body with Cavities Filled with Fluid

This paper studies the motion in a Newtonian force field of a rigid body with fluid-filled cavities and a fixed point, using previously established equations and integrals for the system. Under specified relations among the principal inertia coefficients and parameters describing the force field and…

A PARTICULAR SOLUTION OF THE EQUATIONS OF THE THEORY OF IDEAL PLASTICITY IN CYLINDRICAL COORDINATES

This paper derives a particular solution of the ideal plasticity equations in cylindrical coordinates under the Huber-Mises yield criterion. Assuming selected independence of the strain-rate tensor and shear stress components from the radial and axial coordinates, the displacement, strain-rate, and …

Method for Calculating Three-Dimensional Flow Past Bodies with a Detached Shock Wave

This paper generalizes a previously developed numerical method for supersonic gas-dynamic flow past blunt bodies with detached shock waves to three-dimensional configurations with a plane of symmetry. The method introduces a transformed radial coordinate between the body and the unknown shock surfac…

Complex Plane Strain

This paper develops a plane plastic deformation model for a material whose hardening from infinitesimal slip is anisotropic and depends logarithmically on the angular separation between slip and shear directions. Under standard plane plasticity assumptions, the authors derive an integral equation fo…

On New Particular Solutions of the Problem of the Motion of a Heavy Rigid Body About a Fixed Point

This paper studies periodic motions of a heavy rigid body about a fixed point under rapid rotation, using the Euler-Poisson equations reduced to a quasilinear autonomous system with two degrees of freedom. It derives new particular periodic solutions for the resonant case in which the parameter omeg…

On the Critical External Pressure on a Convex Shallow Shell

This note examines the loss of stability of a shallow strictly convex elastic shell subjected to uniform external pressure, with the aim of estimating the critical pressure at which buckling begins. Using assumptions about supercritical deformation, the shell is divided into nearly undeformed, displ…

On the Possible Influence of the Diffusive Flux of Reaction Products from a Flame on the Decomposition of the Condensed Phase

This paper examines whether gas-phase combustion products diffusing from a flame can influence the decomposition rate of a condensed propellant phase, in addition to the commonly considered heat flux from the flame. It argues that, because heat transfer from the flame is accompanied by a diffusive f…

Green's Tensor for an Anisotropic Elastic Medium with Sources of Internal Stresses

The paper constructs a Green tensor representation for stresses in an anisotropic elastic medium containing sources of internal stress, such as dislocations, point defects, or temperature gradients. Starting from Kröner’s formulation in terms of the incompatibility tensor, it develops an explicit pr…

Generation of High-Velocity Gas Jets

The paper describes an explosive-driven device for producing high-velocity gas jets and strong shock waves by accelerating a metal plate against a gas-filled compression chamber with an outlet diaphragm. Experiments using photochronographic measurements show that gas acceleration occurs mainly in th…

Stationary Resonant Regimes of Certain Rotational Motions

The paper studies rotational motions with one degree of freedom and slowly varying parameters when the small perturbation depends periodically on time. Using a resonant change of variables and averaging methods, it derives equations for stationary resonant regimes characterized by integer frequency …

Two Particular Solutions of the Problem of the Motion of a Body with a Fixed Point

The paper studies the motion of a rigid body with a fixed point when the center of gravity and the vector representing internal cyclic motion lie along a principal axis of inertia. Starting from the equations of motion and their known integrals, it presents two explicit particular solutions in which…

ON THE ASYMPTOTIC TYPE OF PLANE-PARALLEL FLOW IN THE NEIGHBORHOOD OF THE CENTER OF A LAVAL NOZZLE

The paper studies plane-parallel transonic gas flow near the throat center of a Laval nozzle for Cauchy data in which the axial velocity behaves as a power law with exponent between 1 and 2. Using self-similar variables, the governing transonic equations are reduced to an ordinary differential equat…

On a Scheme of the Numerical Method of Characteristics

This paper presents a layer-by-layer scheme for the numerical method of characteristics intended to simplify computation of steady supersonic gas flow around three-dimensional bodies between a shock wave and the body surface. The authors formulate the approach in transformed coordinates and test it …

Analysis of Mathematical Models of Condensed-Phase Combustion

This paper analyzes mathematical models for combustion of a condensed phase, emphasizing cases in which an exothermic reaction within the condensed material contributes substantially to propagation of the combustion front. The authors formulate a boundary-value problem for the temperature profile an…

On Extremal Paths of Plastic Deformation

This paper studies extremal paths of plastic deformation in a hardening material whose yield surface is defined by a loading function depending on stress, plastic strain, and a hardening parameter given by the length of the plastic strain path. Using the associated flow law and variational calculus,…

ON THE CALCULATION OF THE BOUNDARY LAYER OF A COMPRESSIBLE FLUID WITH SLIP BOUNDARY CONDITIONS

The paper addresses the calculation of compressible boundary layers over flat and axisymmetric bodies when velocity and temperature slip conditions are imposed at the wall. Using Dorodnitsyn variables, it argues that, under assumptions including constant slip parameter and a specified temperature ju…