Stress–strain state of a composite anisotropic plate with curvilinear cracks and thin rigid inclusions

A complexpotential solution of a mixed problem of the linear theory of elasticity is given for an infinite plate composed of two anisotropic halfplanes. The plate contains cuts and thin undeformable inclusions shaped like arbitrary open smooth curves that do not intersect each other and the interface between the halfplanes.     

Stability and Self‐Oscillations of a Rotor Containing a Conducting Liquid in a Magnetic Field

This paper considers the problem of the stability in the small of the steadystate spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the buttend boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was Dpartitioned into regions with different degrees of instability is constructed. Steadystate spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steadystate spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steadystate spinning can be subcritical or supercritical.     

Exact solutions and mathematical properties of boundary‐value problems for dynamic‐diffusion boundary layers

The paper studies boundaryvalue problems for dynamicdiffusion boundary layers occurring near a vertical wall at high Schmidt numbers and for dynamic boundary layers whose inner edge is adjacent to the dynamicdiffusion layers. Exact solutions for boundary layers at small and large times are derived. The wellposedness of the boundaryvalue problem for a steady dynamicdiffusion layer is studied.     

Analytical Modeling of Nonaqueous Phase Liquid Dissolution with Green's Functions

Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multidimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semiinfinite and infinite media. The GFM is applied to analytically model multidimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first, second, or thirdtype boundary or source input conditions. Away from the source, the first and thirdtype condition cannot be expected to represent the exact surface condition. The secondtype condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the thirdtype condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.     

Description of a Flow of a Gas‐Condensate Mixture in an Axisymmetric Capillary Tube by the Density‐Functional Method

An isothermal flow of a twophase multicomponent mixture through a smalldiameter capillary tube is examined by the densityfunctional method. For low ratios of the characteristic radius of the capillary to its length, a general form of the dominating term in the asymptotic solution is found. An improved version of the law of mixture transfer is obtained. The form of possible corrections to the Darcy law for the filtration rates of the phases is discussed.     

Estimation of the Effective Absorptivity of Metals from the Observation of Their Martensitic Restructuring under Laser Radiation

A new experimental method is proposed for determining the effective absorptivity of a metal under pulsed laser radiation. The method is based on solving an axisymmetric boundaryvalue heatconduction problem for a halfspace with the use of metallographically measured sizes of the polymorphictransformation zone in the irradiated material. The method is tested on singlecrystal cobalt and St.45 steel samples.     

Nonsimilar Solutions for Mixed Convection in Non‐Newtonian Fluids Along a Vertical Plate in a Porous Medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in powerlaw type nonNewtonian fluids along a vertical plate with powerlaw wall temperature distribution. The mixed convection regime is divided into two regions, namely,the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.     

Hydrodynamic calculations of layered seams on the basis of modified relative permeabilities

The possibility of reducing the dimensionality of the problem of twophase filtration in layered seams by introducing modified phase permeabilities instead of initial relative permeabilities, which are coefficients of the initial system of equations within the framework of the Barkley–Leverett model, is studied. Modified permeabilities are proposed for the case where the relative permeabilities of each phase are represented by analytical dependences for individual interlayers. Onedimensional numerical calculations with these permeabilities are in good agreement with the solution of the twodimensional problem.     

Velocity Measurements in a One‐Dimensional Steady Flow by Methods of Emission Tomography

A new method for velocityfield measurements in a onedimensional steady flow is proposed. The method is based on principles of laserinduced fluorescence combined with emission tomography. Results of a numerical experiment are presented.     

Effect of Porous Coatings on Stability of Hypersonic Boundary Layers

The influence of ultrasoundabsorbing coatings on stability of hypersonic boundary layers is considered. Two types of coatings were used in experiments: feltmetal with a random porous microstructure and a sheet perforated by blind cylindrical microchannels. The experiments were performed in a wind tunnel at a Mach number M = 5.95 on sharp cones with a 7° apex halfangle. Evolution of natural disturbances and artificially induced wave packets in the boundary layer was studied with the help of hotwire anemometry. Spatial characteristics of artificial disturbances were obtained. It is demonstrated that such coatings exert a stabilizing effect on secondmode disturbances.     

Numerical Analysis of Branched Shapes of Arches in Bending

Nonlinear boundaryvalue problems of plane bending of elastic arches under a uniformly distributed load are solved by the shooting method. The problems are formulated for a system of six firstorder ordinary differential equations with a finiterotation field independent of displacements. Simply supported and clamped cases are considered. Branching solutions of the boundaryvalue problems are obtained. For a simply supported arch, a set of solutions describes symmetric and nonsymmetric shapes of bending, which correspond to positive, negative, and zero loads. For a clamped arch, the set of solutions consists of symmetric shapes that occur only for positive loads.     

Numerical analysis of axisymmetric buckling of conical shells

Nonlinear boundaryvalue problems of axisymmetric buckling of conical shells under a uniformly distributed normal pressure are solved by the shooting method. The problems are formulated for a system of six firstorder ordinary differential equations with independent rotation and displacement fields. Simply supported and clamped cases are considered. Branching solutions of the boundaryvalue problems are studied for different pressures and geometrical parameters of the shells. The nonmonotonic and discontinuous curves of equilibrium states obtained show that collapse, i.e., snapthrough instability is possible. For a simply supported shell, multivalued solutions are obtained for both external and internal pressure. For a clamped thinwalled shell, theoretical results are compared with experimental data.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Stationary Simple Waves on a Barotropic Liquid Shear Flow

Stationary threedimensional flows of a barotropic liquid in a gravity field are considered. In the shallowwater approximation, the Euler equations are transformed into a system of integrodifferential equations by the EulerLagrange change of coordinates. A system of simplewave equations is obtained, for which the theorem of existence of a solution attached to a given shear flow is proved. As an example, a particular solution analogous to the solution of the problem of a gas flow around a convex angle is given.     

Propagation of Linear Waves in Gas‐Saturated Porous Media with Allowance for Interphase Heat Transfer

The effect of gas–skeleton heattransfer processes on propagation of fast and slow waves in a porous medium is examined. Frequency intervals are identified, in which attenuation of waves in a gassaturated porous medium is mainly controlled by the heattransfer processes.     

Self‐Equilibrated Stress Fields in a Continuous Medium

It is proved that the solutions of the static equations of a continuous medium constructed in terms of a stress function are selfequilibrated. From a mathematical point of view, these functions can be treated as the connectivity coefficients of the intrinsic geometry of the medium. It is shown that from a physical point of view, the existence of selfequilibrated stress fields is due to a nonuniform entropy distribution in the medium. As an example, for a circle in polar coordinates and a cylindrical sample, a selfequilibrated stress field and an elastic field compensating for its surface component are constructed and it is shown how to write the equation for the intrinsic geometrical characteristics.     

Approximate Solution of an Axisymmetric Contact Problem with Allowance for Tangential Displacements on the Contact Surface

A structurally nonlinear contact problem of a punch shaped like a paraboloid of revolution is studied. An equation for the contactpressure density is derived with allowance for the radial tangential displacements of the boundary points of an elastic halfspace. A method for constructing a closedform approximate solution is proposed. The effect of the tangential displacements on the main contact parameters is discussed.     

Modeling of the Front of Melting and Destruction of a Melt Film During Gas‐Laser Cutting of Metals

The products of laser cutting of metals on an automated laser setup are investigated. Results of model experiments are presented, where soft wax was used instead of metal transforming into the melt; soft wax filled a narrow flat slot between two glass plates and was removed by a heated air stream. The physical processes of melting of the liquidwax film, its destruction, and entrainment by the gas jet being assumed to be analogous to the processes of metalmelt spraying inside the cut in fullscale experiments, the characteristic size of drops formed thereby is evaluated. The modeling results are in qualitative agreement with the results of fullscale experiments. It is shown that the quality of laser cutting of metals directly depends on the character of spraying of the liquid melt and the process of its removal.     

Adjoint problems of mechanics of continuous media in gas‐laser cutting of metals

A mathematical model of gaslaser cutting of metal plates in an inert gas is proposed. The formation and flow of the liquid metal melt film at the cutting front is considered within the framework of incompressible boundarylayer equations. Based on the resultant analytical solution, a local law of energy conservation on the cutting surface is derived, which takes into account the meltfilm thickness and the temperature dependence of thermophysical parameters of the metal. The problem of the cutting shape and depth is solved in the twodimensional formulation. A comparison with experimental data is made in terms of the cutting depth and maximum cutting velocity for carbon and alloy steel.