Transition radiation in two-dimensional elastic systems

Institute of Mechanical Engineering, Russian Academy of Sciences, Nizhnii Novgorod 603024. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 170–178, May–June, 1995.     

Analysis of the applicability of a modified Kol'skii's method for dynamic tests of soils in a deformable casing

Results of an experimental and theoretical analysis of Kol'skii's method for dynamic tests of soft soils in an elastic casing are presented. The model proposed by S. S. Grigoryan for a plastically compressible medium with parameters determined in shock-wave experiments was used as the model of a soft soil. The high-rate deformation of the soil was simulated using a modified “Dunamics-2” program package. The numerical calculations performed showed that the compliance of the casing and friction practically do not influence the measured characteristics of the soil and the basic premises of Kol'skii's method are adequate for soft soil too. Institute of Mechanics, Nizhinii Novgorod State University, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 155–162, May–June, 2000.     

Numerical modeling of three-dimensional shear flow in a cavity with moving lids

The results of a numerical calculation of the unsteady shear flow of a viscous incompressible fluid in a cavity with moving lids are given for various geometries and values of the Reynolds number. The paper describes the numerical method developed for solving the three-dimensional unsteady Navier-Stokes equations in a regular domain and also the direct method of parallelling the solution for a multiprocessor computer with distributed memory. Test results are compared with the results of other authors. Moscow, Nizhnii Novgorod, Marseille. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 41–49, May–June, 1998.     

Ballistic magnetocumulative generator

The reusable source of a pulsed magnetic field—a ballistic magnetocumulative generator (BMG)—is considered. Electrical engineering analysis of the efficiency of operation of the generator on an active-inductive load is performed. A method for calculating the two-dimensional distribution of the field in the busbars of the generator is developed. Experimental results are obtained for the operation of aBMG model on some types of load. Central Scientific-Research Institute “Burevestnik,” Nizhnii Novgorod 603603. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 22–29, May–June, 1998.     

Flow structures and heat transfer in anisotropic annular porous interlayers

The results of calculating the flow and heat transfer in annular porous interlayers are presented as functions of the Rayleigh number, the geometry of the interlayer, and the anisotropy of the permeability. The existence of single-vortex and multivortex convection regimes depending on the permeability anisotropy coefficient is established and their importance for the effectiveness of the heat-insulating properties of cylindrical interlayers is shown. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–128, July–August, 1998. The work was carried out with support from the Russian Foundation for Basic Research (project No. 96-01-000584).     

Plane waves in a heavy two-layer liquid excited by a cylinder moving at an angle to the horizontal

A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated. The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with a constant acceleration and an oscillating cylinder is constructed analytically. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August, 1998.     

Nonlinear development of two-dimensional hydroelastic instability in a turbulent boundary layer on an elastic coating

Nonlinear evolution of hydroelastic instability arising in the flow past a coating of a rubber-type material by a turbulent boundary layer of an incompressible fluid is studied. A nonlinear dispersion equation for two-dimensional, quasi-monochromatic, low-amplitude waves is derived. The Prandtl equations for the mean (over the waviness period) boundary-layer flow are solved in the approximation of local similarity and by direct numerical integration. Evolution of unstable waves in time is studied on the basis of the Landau equation, which is derived separately for the instability of fast waves (flutter) and the quasi-static instability (divergence). The calculation results are compared with available experimental data. Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 69–80, July–August, 2000.     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

Nonlinear characteristics of the interaction of a turbulent boundary layer with a wavy surface

A nonlinear interaction of a turbulent boundary layer with a wavy surface of a solid body or a liquid whose level has a deviation in the form of a traveling monochromatic wave is studied. For the waviness of small curvature, a calculation procedure is proposed for the amplitude dependence of the drag coefficient and complex elasticity which characterizes the back action of the flow on the surface inflection. The analysis is based on the use of an isotropic algebraic model of turbulent viscosity and an orthogonal system of curvilinear coordinates that follow the surface inflections. The interaction between the flow and the surface wave is described within the framework of a quasi-linear model, and a two-scale, mean-flow model is used to determine the transverse structure of the flow in a smoothly expanding boundary layer. Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 72–84, November–December, 1998.     

Investigation of the effect of microgravity on convection and mass transfer during crystal growth from aqueous solution

The modeling process is described and the results obtained on earth and in microgravity are compared. The effect of reduced gravity on the uniformity of the layer adjacent to the growing crystal is investigated. It is shown how, by using the results of modeling in microgravity, the parameters characteristic of optimal solution hydromechanics under terrestrial conditions can be estimated.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–66, September–October, 1994.     

Comparison of the drag coefficients of bodies moving in liquids with various stratification profiles

For bodies moving in liquids with various stratification profiles, the relation between the drag coefficients considered as functions of the Froude number is investigated. The problems of stratified liquid dynamics have not previously been studied from this viewpoint, either experimentally or theoretically. On the range of the Froude numbers F₁-1, the drag force coefficients obtained from bench measurements of the towing resistance to the uniform horizontal motion of models in two-layer and continuously stratified liquids are compared. The experimental data obtained in a thermocline are then compared with the results of [1,2] for linearly stratified and two-layer liquids.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–11, July–August, 1996.     

Symmetry Reduced Dynamics of Charged Molecular Strands

The equations of motion are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that these equations are nonlocal when the screened Coulomb interactions, or Lennard–Jones potentials between pairs of charges, are included. The nonlocal dynamics is derived in the convective representation of continuum motion by using modified Euler–Poincaré and Hamilton–Pontryagin variational formulations that illuminate the various approaches within the framework of symmetry reduction of Hamilton’s principle for exact geometric rods. In the absence of nonlocal interactions, the equations recover the classical Kirchhoff theory of elastic rods. The motion equations in the convective representation are shown to arise by a classical Lagrangian reduction associated to the symmetry group of the system. This approach uses the process of affine Euler–Poincaré reduction initially developed for complex fluids. On the Hamiltonian side, the Poisson bracket of the molecular strand is obtained by reduction of the canonical symplectic structure on phase space. A change of variables allows a direct passage from this classical point of view to the covariant formulation in terms of Lagrange–Poincaré equations of field theory. In another revealing perspective, the convective representation of the nonlocal equations of molecular strand motion is transformed into quaternionic form.     

Analytic investigation of a nonlinear problem of the effect of buoyancy on the evolution of an annular vortex

The evolution of a heavy axisymmetric vortex whose density differs from that of the surrounding irrotational ideal fluid is investigated analytically. If the vortex had no buoyancy (i.e., if the densities were identical), it would preserve its shape and velocity. An approximate analytic solution of the problem is obtained. This solution describes two types of evolution of the vortex shape corresponding to different values of the initial velocity and small buoyancy. The spectrum of a nonlinear wave developing on the vortex boundary is estimated.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–66, January–February, 1996.     

Homogenization of the signorini boundary-value problem in a thick plane junction

We consider a mixed boundary-value problem for the Poisson equation in a plane thick junction Ω_ε that is the union of a domain Ω₀ and a large number of ε-periodically located thin rods. The nonuniform Signorini conditions are given on the vertical sides of the thin rods. The asymptotic analysis of this problem is made as ε → 0, i.e., in the case where the number of thin rods infinitely increases and their thickness tends to zero. With the help of the integral identity method, we prove the convergence theorem and show that the nonuniform Signorini conditions are transformed (as ε → 0) into the limiting variational inequalities in the domain that is filled up with thin rods when passing to the limit. The existence and uniqueness of a solution to this nonstandard limit problem are established. The convergence of the energy integrals is proved as well. Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 44–58, January–March, 2009.     

Multivalued solutions of the spatial problems of nonlinear deformation of thin curvilinear rods

We have developed a finite-element model to study the spatial deformation of elastic rods at large displacements. A numerical algorithm for constructing multivalued nonlinear solutions in the presence of many bifurcation and limit points is formulated. Results of a study of the stability supercritical equilibrium forms of elastic rods, which were supported experimentally, are reported. Chaplygin Siberian Aviation Institute, Novosibirsk 630051. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 141–149, March–April, 1998.     

Homogenization of a Boundary-Value Problem with Varying type of Boundary Conditions in a Thick Two-Level Junction

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω _ɛ that is the union of a domain Ω₀ and a large number 2N of thin rods with thickness of order ɛ = (N ⁻¹). Depending on their lengths, the thin rods are divided into two levels. In addition, the rods from each level are ɛ-periodically alternated. Inhomogeneous Neumann boundary conditions are given on the vertical sides of the thin rods of the first level, and homogeneous Dirichlet boundary conditions are given on the vertical sides of the rods of the second level. We investigate the asymptotic behavior of a solution of this problem as ɛ → 0 and prove a convergence theorem and the convergence of the energy integral. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 241–257, April–June, 2005.     

Nonlinear regimes of variation of the shape of an elastic tube containing a flowing fluid

A linear and nonlinear analysis of the distributed oscillations of an elastic tube with a fluid flowing in it is developed. The critical flow velocity and the wavelength and oscillation frequency in the tube-flow system at loss of stability are found. The geometrical and physical nonlinearities, the latter related to increase in the Young’s modulus of the tube wall material with increasing strain, are considered. It is shown that four characteristic regimes of change of tube shape are possible: local dilatation, collapse, flexure, and distributed auto-oscillations. The tube oscillations are analyzed numerically for the nonaxisymmetric case. The conditions of existence of these effects in blood vessels are examined. Nizhni Novgorod, e-mail: klochkov@appl.sci-nnov.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 46–55, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 97-02-18612).     

Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction

We consider a mixed boundary-value problem for a Poisson equation in a plane two-level junction Ω_ε that is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order . The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The homogeneous Dirichlet conditions and inhomogeneous Neumann conditions are given on the sides of the thin rods from the first level and the second level, respectively. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct an asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H ¹(Ω_ε) as ε → 0 (N → +∞). Published in Neliniini Kolyvannya, Vol. 9, No. 3, pp. 336–355, July–September, 2006.     

Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

In this paper, we present a novel approach to quantify regular or chaotic dynamics of either smooth or non-smooth dynamical systems. The introduced method is applied to trace regular and chaotic stick–slip and slip–slip dynamics. Stick–slip and slip–slip periodic and chaotic trajectories are analyzed (for the investigated parameters, a stick–slip dynamics dominates). Advantages of the proposed numerical technique are given.     

Structures and regimes of shear flow in a plane cavity with translating boundaries

Stability of shear flow in a plane cavity whose boundaries translate in opposite directions is analyzed by solving the nonstationary Navier-Stokes equations numerically. It is shown that, depending on the Reynolds number and the cavity aspect ratioH/R, there may exist either a single-vortex, or a multi-eddy, or an intermediate flow regime with a bridge, all of which are stable. No oscillatory regime was found forH/L=0.1–10 and Re=1–3000.Nizhnii Novgorod, Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–56, March–April, 1995.