Existence of a new type of irregular shock-wave interaction

Several types of plane shock-wave interactions [1–5], realized in various cases of practical importance, are now known. In [7] the possibility of the existence of a new type of shock-wave interaction was demonstrated by numerically solving the axisymmetric boundary-value problem. Here, the corresponding two-dimensional boundary-value problem of the interaction between a shock wave and a plane shock is numerically studied, a theoretical basis is obtained for the region of existence of the shock-wave interaction detected, and its principal properties are investigated. Moscow, Dnepropetovsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1988.     

Interaction of a die with a layered elastic foundation

Plane and axisymmetric contact problems for a three-layer elastic half-space are considered. The plane problem is reduced to a singular integral equation of the first kind whose approximate solution is obtained by a modified Multhopp-Kalandiya method of collocation. The axisymmetric problem is reduced to an integral Fredholm equation of the second kind whose approximate solution is obtained by a specially developed method of collocation over the nodes of the Legendre polynomial. An axisymmetric contact problem for an transversely isotropic layer completely adherent to an elastic isotropic half-space is also considered. Examples of calculating the characteristic integral quantities are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 165–175, May–June, 2006.     

On the stress-strain state of a transversally isotropic body with a paraboloidal inclusion

A closed solution is presented for the three-dimensional problem of the stress-strain state of an unbounded elastic body with a soldered-in transversally isotropic inclusion in the form of a paraboloid of revolution. Here, it is assumed that the body is under axisymmetric tension (compression). A solution of the corresponding problem for a paraboloidal recess is obtained as a special case. Podil’chuk [2, 3] has investigated similar problems for isotropic bodies with an inclusion assuming the form of a paraboloid of revolution or an elliptical paraboloid. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 16–22, November, 1998.     

Separationless flow past a body of revolution with simultaneous suction and ejection of fluid

The problem of the axisymmetric potential flow past a body of revolution with a channel along the axis in the presence of a recirculation flow zone near the body, first proposed by G. Yu. Stepanov, is solved. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 14–21, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00123).     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.     

Dynamic compaction model for a granular medium

A model for dynamic compaction of granular medium is proposed for the case in which the external action far exceeds the yield strength of the material. A radial axisymmetric compaction problem is solved for a granular medium with nanosize structure in the presence of a rigid rod at the symmetry axis. Simulated data are compared with experimental data on magnetic pulsed compaction of oxide nanopowders. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 211–215, March–April, 2008.     

Some primal problems of the axisymmetric theory of elasticity for space with a flat slit bounded by a circle

We consider the first and second primal problems of the axisymmetric theory of elasticity for space with a round slit and a mixed problem in which forces are specified on one side of the slit and displacements are specified on the other side. The problems reduce to conjugation problems for generalized analytic functions on rectilinear segments, whose solution is obtained in closed form. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 117334. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1 pp. 144–151, January–February, 2000.     

Quasi-cylindrical figures of equilibrium of a rotating fluid

The problem of the equilibrium shape of a steady rotating rectilinear infinite cord of ideal self-gravitating homogeneous fluid is considered. The question whether, apart from the obvious solution, namely, an infinite circular cylinder, noncylindrical equilibrium figures can exist is investigated. A search is carried out among axisymmetric figures with periodic surface structure (“wavy” cylinders). The period of the wave structure and, in the first approximation, the shape of the surface are found as functions of the angular velocity of rotation. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–30, May–June, 2000.     

The paraxial approximation for a dense electron beam

Approximate equations are derived for a narrow (paraxial) electron beam with a three-dimensional axis; these equations generalize the familiar equations [1] to the case in which the field of the charge in the beam is important. A class of beams is distinguished for which the problem reduces to ordinary differential equations. The paraxial approximation for a narrow beam of electron trajectories in a given field is well known for the case in which the characteristic dimension L_* of the irregularities is much greater than a_*, the characteristic width of the beam. The field of a three-dimensional beam can be included in the equations [1] if the beam density ρ is nonuniform over lengths L_*. The self-field of the beam was not actually taken into account in[1]. In this paper we attempt to remedy this deficiency, with partial success for an axisymmetric beam with a rectilinear axis [2]. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 3–10, 1968.     

Self-similar solutions of the problem of displacement of one gas by another in an axisymmetric case with a quadratic drag law

A problem of piston-induced displacement of one gas by another in cracks (porous media) in an axisymmetric case with a quadratic drag law is studied. Self-similar solutions for determining the dynamic characteristics (velocity and pressure) of the displacing and displaced gases are constructed in quadratures. The velocity and pressure are studied as functions of a self-similar variable for several initial conditions and parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 87–92, September–October, 2008.     

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.     

Effect of a thin coating on the pressure distribution in contact problems involving frictional heat generation

A thermoelastic problem for a layer of finite thickness one of whose surfaces is subjected to the action of normal pressure and heat flux is studied. A relationship among vertical displacements of the surface of the layer, the surface temperature, and the disturbing factors is obtained. Corresponding relations are obtained for a layer of small thickness. An axisymmetric contact problem for a rigid heat-conducting base whose surface is coated with a thin elastic layer is studied as an example. Franko L'vov State University, L'vov 290602. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 110–118, January–February, 1998.     

The axisymmetric lamb’s problem for a finite prestrained half-space covered with a finite prestretched layer

The piecewise-homogeneous body model and the three-dimensional linearized theory of elastic waves in prestressed bodies are used to solve the axisymmetric time-harmonic Lamb’s problem for a finite prestrained half-space covered with a finite prestretched layer. It is assumed that the half-space and layer are incompressible and their deformation is described by the Treloar potential. The normal stress at the interface is calculated Published in Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 132–143, March 2007.     

Dynamic edge angles of wetting upon spreading of a drop over a solid surface

The hydrodynamic free-boundary problem of the axisymmetric spreading of a viscous-fluid drop over the smooth surface of a solid under the action of capillary forces and under the conditions of weak gravitation is considered. For finite inclination angles of the free surface and small capillary numbers, the problem is reduced to the simpler hydrodynamic problem in a region with known boundary by the asymptotic method. An expression for the dynamic edge angle of the drop is obtained. It is shown that in addition to the local inclination angle of the boundary near the contact line of three phases, one drop has several dynamic edge angles. These angles are calculated for small Reynolds and Bond numbers. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 101–107, January–February, 1999.     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

The blunt-body problem in a nonuniform hypersonic viscous gas flow

The laws of heat transfer associated with the interaction of underexpanded supersonic gas jets and obstacles or blunt bodies have been investigated, for example, in [1–3]. Similar problems of nonuniform flow occur when bodies move in the wake behind other bodies; however, in this case the laws of heat transfer have so far received little attention [4–8]. It has been established that for a certain Reynolds number and flow nonuniformity parameters a zone of reverse-circulatory flow develops near the front of the blunt body. However, the conditions of transition to separated flow have not been determined. This paper presents a self-similar solution of the equations of the viscous shock layer near the stagnation line in supersonic flow past an axisymmetric blunt body located behind another body. On the basis of this solution a separationless flow criterion is proposed. The effect of the nonuniformity and the Reynolds number on the shock standoff distance, the convective heat flux and the friction drag of the blunt body is investigated. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–125, November–December, 1986. In conclusion the authors wish to thank I. G. Eremeitsev for useful suggestions and G. A. Tirskii for discussing their work.     

Torsion of an elastic space with a semi-infinite conical crack

The axisymmetric problem of stress concentration near a conical crack in an infinite elastic space with a rotation center is addressed. The problem is reduced to an integro-differential equation. Its exact solution is obtained. An expression for the stress intensity factor in crack neighborhood is derived and numerically analyzed for different positions of the rotation center and the crack opening angles __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 99–107, February 2007. For the centenary of the birth of G. N. Savin.     

Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

Nonstationary axisymmetric problem of electroelasticity for a piezoceramic cylinder with circular polarization

This paper considers the problem of the propagation of forced electroelastic axisymmetric torsional waves in a hollow piezoceramic cylinder of finite dimensions, whose curvilinear electroded surfaces are subjected to shear stresses or an electrical potential. A new closed solution is constructed by expansion in vector eigenfunctions using the structural algorithm of finite integral transforms, which makes it possible to determine vibration eigenfrequencies, the stress-strain state of the element, and the potential and intensity of the induced electrical field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 12–21, January–February, 2009.     

Numerical finding of the equilibrium interface of liquids in an axisymmetric vessel

A study is made of the problem of numerical determination of doubly connected axisymmetric equilibrium shapes of the interface of two immiscible liquids in an arbitrary axisymmetric vessel under conditions of reduced gravity. Problems of this kind are of practical interest in connection with the study of the behavior of fuel in the tanks of spacecraft [1]. It is assumed that the liquids are homogeneous and incompressible and have a temperature constant throughout the complete volume. In the investigation of the equilibrium of the interface of liquids under conditions of complete or partial weightlessness, it is necessary to take into account the forces of surface tension, which play a decisive part in such a situation. The equilibrium of liquids in a vessel with allowance for surface tension is described by a system of nonlinear equations [2]. In the present paper, the problem is solved by the Kantorovich— Newton iterative method [3], which makes it possible to reduce the nonlinear problem to a succession of linear problems solvable by the method of finite differences.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–137, September–October, 1981.I thank I. E. Tarapov and I. I. Ievlev for constant interest in the work and helpful comments.