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2013 year, number 4
M. Yu. Plotnikov, A. K. Rebrov
Keywords: supersonic rarefied gas flow, permeable grid, direct simulation Monte Carlo method
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The direct simulation Monte Carlo method is used to study a plane–parallel supersonic gas flow through a grid formed by a series of parallel infinite cylinders. Characteristic features of the shock disturbance formation during the interaction of a supersonic flow with a permeable grid and the effect of this disturbance on the flow parameters behind the grid are revealed. The boundaries of the domain of supersonic flow breakup ahead of the grid and the laws of the total momentum loss on the grid are obtained. Kinetic and energetic characteristics of the flow behind the grid are determined.

S. A. Kinelovskii^{}, K. K. Maevskii^{}
Keywords: shock adiabat, porous heterogeneous medium, powder mixture, thermodynamic equality, additive approximation, GrÃ¼neisen coefficient, alloys
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Within the framework of a thermodynamically equilibrium model, dynamic loading of mixtures of two and more condensed phases with different properties within the experimental error is described by using species parameters only. The behavior of alloys considered as mixtures with the same volume fractions of the species is studied. The behavior of condensed phases for solid and porous materials is described with the use of the equation of state of the Mie–Grüneisen type and with allowance for the dependence of the Grüneisen coefficient on temperature. The calculated results are compared with experimental data and available calculated results in wide ranges of parameters.

V. I. Bukreev, I. V. Sturova, A. V. Chebotnikov
Keywords: seiches, shallow water theory, natural frequencies and modes, laboratory experiment, spectral analysis
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The natural frequencies and modes of seiche oscillations in a closed water reservoir consisting of a long narrow channel connected to a wide basin were investigated theoretically and experimentally. Calculations were made using linear shallowwater theory in twodimensional and onedimensional formulations. The spectral properties of freesurface oscillations at points lying on the nodal lines of the first four modes of seiche oscillations were studied experimentally. The onedimensional model adequately predicts lowermode frequencies, but the data on the positions of the nodal points of seiche oscillations obtained using this model are somewhat different from those obtained experimentally and using the twodimensional model.

A. N. Baikin^{}, S. V. Golovin^{}
Keywords: cylindrical vortex, electrically conducting fluid, magnetic hydrodynamics, exact solutions
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An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.

A. E. Medvedev
Keywords: viscous incompressible fluid, Navier–Stokes equations, analytical solution, Poiseuille flow
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A flow of a viscous incompressible fluid in a deformable tube is considered. Solutions of unsteady threedimensional Navier–Stokes equations are obtained for lowReynoldsnumber flows in the tube (under the condition of small deformations of the wall): generalized peristaltic flow and flow with elliptical deformations of the vessel walls. At small unsteady deformations of the tube walls, the solutions satisfy the equations and boundary conditions with an error smaller than the tube wall deformation level by an order of magnitude. In the case of elliptical deformations of the vessel, the solution agrees well with experimental data.

A. F. Kurbatskii^{}, L. I. Kurbatskaya^{}
Keywords: turbulence, intermittency, stable stratification, boundary layer
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The flow structure and statistical features of a turbulent stable stratified boundary layer are studied by using the Reynoldsaveraged Navier–Stokes (RANS) scheme of turbulence, which takes into account the influence of internal gravity waves. The possibility of the RANS description of intermittent turbulence both near the surface and above the surface in the vicinity of the lowlevel jet flow formed above the boundary layer is analyzed. The role of turbulent diffusion (thirdorder statistical moments) in intermittent turbulence generation is discussed. Numerical results are demonstrated to agree with results of LES modeling and actual observations. Intermittency of turbulent kinetic energy both near the surface and above this surface in the vicinity of the lowlevel jet flow is revealed.

S. V. Lukashevich, S. O. Morozov, A. N. Shiplyuk
Keywords: experiment, hypersonic boundary layer, second mode of disturbances, passive porous coating
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The effect of passive porous coatings of different lengths on the second mode of disturbances in a hypersonic boundary layer is considered. The experiments are performed in a flow with a freestream Mach number M_{∞} = 5,8 and five values of the unit Reynolds number around a sharp cone with an apex halfangle equal to 7°, which is aligned at a zero angle of attack. One half of the model surface along its generatrix is covered by a porous material, and the other part is a solid surface. Pressure fluctuations on the model surface are measured. It is found that application of a passive porous coating can either decrease or increase the amplitude of the second mode. The length of the passive porous coating corresponding to the maximum efficiency of its action on flow disturbances and the coating length that increases the amplitude of the second mode are found.

B. Kh. Eshmatov, Kh. Eshmatov, D. A. Khodzhaev
Keywords: Kirchhoff–Love hypothesis, composite materials, viscoelastic rectangular plate, viscoelastic cylindrical panel, concentrated mass, Bubnov–Galerkin method, nonlinear flutter
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The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δDirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov–Galerkin method. The resulting system with a weakly singular Koltunov–Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.

G. V. Kuznetsov, V. I. Maksimov, M. A. Sheremet
Keywords: natural convection, experiment, Fluent software package, conjugate heat transfer, closed parallelepiped, local energy source
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An experimental and numerical analysis was performed to investigate the laminar regimes of conjugate thermogravitational convection in a closed parallelepiped with heatconducting walls of finite thickness in the presence of a local energy source with convective heat exchange with the environment. The numerical studies were performed using the Fluent software. The experimental data and numerical results agree well each other.

M. A. Pakhomov, V. I. Terekhov
Keywords: Eulerian and Lagrangian approaches, separated gas–droplet flow, turbulence, dispersion and evaporation of droplets
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The Eulerian and Lagrangian approaches are used to perform a numerical study of the disperse phase dynamics, turbulence, and heat transfer in a turbulent gas–droplet flow in a tube with sudden expansion with the following ranges of twophase flow parameters: initial droplet size d_{1} = 0–200 μm and mass fraction of droplets M_{L1} = 0–0.1. The main difference between the Eulerian and Lagrangian approaches is the difference in the predictions of the droplet mass fraction: the Eulerian approach predicts a smaller value of M_{L} both in the recirculation region and in the flow core (the difference reaches 15–20%). It is demonstrated that the disperse phase mass fraction calculated by the Lagrangian approach agrees better with measured data than the corresponding value predicted by the Eulerian approach.

V. P. Bushlanov, I. V. Bushlanov, E. N. Sentyakova
Keywords: Darcy's law, permeability coefficient, specific surface area
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Using the equation of living forces averaged over the volume of the filter and obtained from the Navier–Stokes equations of an incompressible fluid, an analytical formula for the permeability coefficient in the classical Darcy problem is derived to within the principal terms of the Poiseuille number. It is shown that the resulting permeability coefficient is inversely proportional to the square of the specific surface area and the dimensionless average dissipation rate of the kinetic fluid energy in the filter.

V. L. Kotov, V. V. Balandin, A. M. Bragov, E. Yu. Linnik, V. V. Balandin
Keywords: quadratic localinteraction model, friction, conical projectile resistance force deployment, penetration, sandy soil, Grigoryan model, Hugoniot sphericalcavity expansion
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A localinteraction model describing the penetration of axisymmetric projectiles into sandy soil at a constant velocity is studied experimentally and theoretically. Two approaches to the determination of the parameters of the quadratic localinteraction model are considered. The first approach is based on the use of the solution of the problem of sphericalcavity expansion taking into account the dynamic compressibility and shear resistance of soil. In the second approach, model parameters are determined based on the experimental dependence of the resistance to penetration of conical projectiles into a sandy soil on the impact velocity. Good agreement was obtained between the results of experiments, twodimensional numerical calculations, and calculations for the local interaction model based on the solution of the sphericalcavity expansion problem and used to determine the maximum resistance to penetration of conical and spherical projectiles.

A. Sadeghi
Keywords: atomic force microscope cantilever, tapered Timoshenko beam, resonant frequency
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The resonant frequency of flexural vibrations for a double tapered atomic force microscope (AFM) cantilever has been investigated by using the Timoshenko beam theory. In this paper, the effects of various parameters on the dimensionless frequency of vibrations of the AFM cantilever have been studied. The differential quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when the Timoshenko beam parameter or the cantilever thickness increases, and highorder modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higherorder modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Furthermore, with increasing the breadth taper ratio, the frequency increases. The DQM results are compared with the exact solution for a rectangular AFM cantilever.

Yu. V. Nemirovsky, T. P. Romanova
Keywords: ice plate, rigidplastic model, curvilinear contour, rigid insert, incompressible foundation, ultimate load, material with different tensile and compressive ultimate stresses
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A method is developed for determining the loadbearing capacity of ice plates, which are modeled by an ideal rigidplastic plate located on an incompressible foundation. The plate with a simply supported or clamped arbitrary smooth curvilinear contour is subjected to a load uniformly distributed over an arbitrarily shaped reinforced local central region. An analytical expression for the ultimate load is derived. A plate shaped as an ellipse is considered as an example.

M. N. Saushkin, V. P. Radchenko, A. Yu. Kurov
Keywords: hollow cylindrical specimen, surface plastic deformation, semicircular notch, distribution of residual stresses, finite element method
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A method is proposed to study the distribution of residual stresses in a semicircular notch in a hollow cylindrical specimen after advanced surface plastic deformation. The initial information used in the method is one or two experimentally determined components of the residual stress tensor in the hardened layer of the smooth specimen. The problem is solved using a finite element technique taking into account initial plastic strains, which are set in correspondence to the residual stresses according to the laws of elasticity. The effect of the hardening technology and notch depth on the distribution of residual stresses is studied. Experimental verification of the method showed that the calculated and experimental data on the stress distribution over the depth of the layer are in good agreement.

L. A. Tkacheva
Keywords: surface waves, flexuralgravity waves, elastic plate, added masses, damping coefficients, eigenfrequencies and oscillation modes, the method of normal modes, integral equations, boundary element method
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The problem of the interaction of surface and flexuralgravity waves with a vertical barrier is solved in a twodimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.

N. P. Lazarev
Keywords: plate, crack, cut, nonpenetration condition, variational problem
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The condition of mutual nonpenetration of the crack faces is proposed for a Timoshenko plate with an oblique crack, whose initial state is defined by a surface the normal to which makes a small angle with the middle plane. Unique solvability of the variational problem of plate equilibrium with the nonpenetration conditions for the crack faces specified on the curve describing the crack is proved. A differential formulation of the problem equivalent to the original formulation for sufficiently smooth solutions is proposed. For the onedimensional case (beam with a cut), an analytical solution is obtained, and the cases of longitudinal tension and compression are examined.

G. G. Savenkov, B. K. Barakhtin, A. M. Bragov, E. V. Shchukina
Keywords: mild steel, mechanical properties, dynamic bending, fractal dimension
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The mechanical properties of notched samples of St.10 steel under tension at different strain rates were studied. Fracture surfaces of the notched samples after the dynamic bending were investigated, the mechanisms of plastic deformation and fracture were determined, and the fractal dimension of the fracture contours were obtained.

Yu. P. Meshcheryakov, A. A. Pikarevskii, O. I. Stoyanovskii
Keywords: explosion chamber, pulse loading, numerical calculation, shockabsorbing pad, strain measurement, vibration damping parameter
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The effect of stiffness of shockabsorbing pads of a real explosion chamber on the degree of vibration damping and maximum stresses in the body of the camera is experimentally and numerically investigated. The results are analyzed. A relation between the seismic effect on the foundation after a charge explosion inside the chamber and durability of its operation is revealed.

