Analysis of functionally graded thick truncated cone with finite length under hydrostatic internal pressure

Finite Element Method based on Rayleigh–Ritz energy formulation is applied to obtain the elastic behavior of functionally graded thick truncated cone. The cone has finite length, and it is subjected to axisymmetric hydrostatic internal pressure. The inner surface of the cone is pure ceramic and the outer surface is pure metal, and the material composition varying continuously along its thickness. Using this method, the effects of semi-vertex angle of the cone and the power law exponent on distribution of different types of displacements and stresses are considered.     

Edge waves in a shallow fluid beneath a fractured elastic plate

It is shown that a fracture in an elastic plate floating on the surface of a shallow liquid layer is a waveguide along which wave energy can be transported. The edge wave velocity is less than the velocity of flexural-gravity waves. The existence of an antisymmetric edge wave mode depends on the Poisson's ratio of the elastic plate. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–189, July–August, 1994.     

Invariant sets and comparison of dynamical systems

We propose a method for the construction and investigation of invariant sets of differential systems described by cone inequalities with the use of the operator of differentiation along the trajectories of the system. Well-known conditions for the positivity of linear and nonlinear differential systems with respect to typical classes of cones are generalized. A method for comparison and ordering is developed for a family of dynamical systems. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 163–176, April–June, 2007.     

Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c _p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.     

Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.     

Instability of entangled polymers in cone and plate rheometry

Flow instability in three entangled polymer systems including a 10 wt% 1,4-polybutadiene (PBD) solution, an 11.4 wt% polyisobutylene (PIB) solution, and a long chain branched polyethylene melt (LD 146) was investigated in both stress-controlled and rate-controlled experiments in the cone–plate geometry. It was found that flow instability occurred for experiments in both rate- and stress-controlled modes. The effects of cone angle or rim gap and shearing time on flow instability were studied. The smaller cone angle and shorter shearing time delay (in terms of stress or shear rate) the occurrence of severe instability and mass loss of the PBD solution but not for the PIB. Our data are consistent with the dramatic shear rate jump for the flow curve constructed from the stress-controlled experiments being associated with mass loss after the severe instabilities. We also find that the Cox–Merz representation gives a powerful tool for investigation of flow instability. Finally, another interesting result in this work is that it seems that the stress overshoot can be related to the onset of flow instability in the present system.     

Influence of discrete ribs on the vibrations of rectangular plates

A rectangular plate reinforced with longitudinal ribs is considered. The influence of the discrete ribs on the wavenumbers of harmonic waves propagating along the ribs is investigated. The effect of the stiffness parameters of the ribs on the natural frequencies and modes of a cross-ribbed plate is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 65–78, February 2006.     

Supersonic radial flow past sharp-nosed cones

Axisymmetric and three-dimensional gas flows past sharp cones are studied both analytically and numerically for the case in which the supersonic oncoming stream is of source type. The effect of the governing parameters, such as the distance from the source to the cone, the specific heat ratio, the cone angle, and the angle of attack, on the flow is studied. Asymptotic laws governing the flow at large distances from the cone vertex are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 112–120, March–April, 1994.     

Stress-strain state of an anisotropic plate with curvilinear cracks and thin rigid inclusions

A mixed problem of linear elasticity for an infinite anisotropic plate with cuts and thin undeformable inclusions located along arbitrary open smooth curves is solved with the use of complex potentials. Special representations of the solutions are constructed and a governing system of singular integral equations is obtained. A numerical algorithm for determining the stress-strain state of the plate, including the stress-intensity factors at the tips of cuts and rigid inclusions, is proposed. Calculation results are given. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 213–219, May–June, 2000.     

Vortical structures on a flapping wing

A wing in the form of a rectangular flat plate is subjected to periodic flapping motion. Space–time imaging provides quantitative representations of the flow structure along the wing. Regions of spanwise flow exist along the wing surface; and depending on the location along the span, the flow is either toward or away from the tip of the wing. Onset and development of large-scale, streamwise-oriented vortical structures occur at locations inboard of the tip of the wing, and they can attain values of circulation of the order of one-half the circulation of the tip vortex. Time-shifted images indicate that these streamwise vortical structures persist over a major share of the wing chord. Space–time volume constructions define the form and duration of these structures, relative to the tip vortex.     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Fine structure of a stratified flow near a flat-plate surface

The pattern of disturbances arising during the motion of a strip along a horizontal surface in a continuously stratified fluid with identified upstream and attached internal waves, boundary layers, and edge singularities is calculated in the liner approximation. The flow pattern behind a flat plate moving with a constant velocity in a continuously stratified fluid is studied with the use of the optical schlieren technique; transformation of waves and finely structured elements of the flow with increasing plate velocity is analyzed. The calculated and experimentally observed patterns of internal waves at low velocities are demonstrated to be in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 77–91, November–December, 2007.     

A study of heat-transfer processes in a supersonic flow around a spherically blunted cone with allowance for injection of a gas-cooler

The heat- and mass-transfer processes of a spherically blunted cone and a supersonic air flow are identified by the methods of solving direct and inverse problems with allowance for the heat flow along the contour and the injection of a gas-cooler. The ranges of applicability of the standard one-dimensional approaches and the method of a thin wall for recovering heat fluxes directed toward the body in flow are shown in the entire time period considered. State University of Tomsk, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 123–132, September–October, 1999.     

EBSD Study of Delamination Fracture in Al–Li Alloy 2090

Aluminum–lithium (Al–Li) alloys offer attractive combinations of high strength and low density for aerospace structural applications. However, a tendency for delamination fracture has limited their use. Identification of the metallurgical mechanisms controlling delamination may suggest processing modifications to minimize the occurrence of this mode of fracture. In the current study of Al–Li alloy 2090 plate, high quality electron backscattered diffraction (EBSD) information has been used to evaluate grain boundary types exhibiting delamination fracture and characterize microtexture variations between surrounding grains. Delamination was frequently observed to occur between variants of the brass texture component, along near-Σ3, incoherent twin boundaries. EBSD analyses indicated a tendency for intense deformation along one side of the fractured boundary. A through-thickness plot of grain-specific Taylor factors showed that delaminations occurred along boundaries with the greatest difference in Taylor factors. Together, these suggest a lack of slip accommodation across the boundary, which promotes significantly higher deformation in one grain, and stress concentrations that result in delamination fracture.     

Stability of conical shells made of composites with one plane of elastic symmetry

The paper proposes a technique for stability analysis of anisotropic laminated thin shells of revolution made of a composite with one plane of symmetry. The technique is used for numerical analysis of truncated cones made of binder-impregnated filaments continuously wound along geodesic lines. It is shown that the effect of low symmetry on the critical loads depends not only on the number of laminas, but also on the cone angle __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 93–101, June 2007.     

Eigenvibrations of a flexible platform floating on shallow water

The spectral problem for a flexible platform (airport) floating on shallow water is examined. The platform is modeded by a flexible plate of finite width and infinite length. A waveguide eigenmode is detected which propagates along the platform and attenuates exponentially away from it. The remaining eigenmodes are outgoing and growing exponentially away from the platform. All the eigenmodes can be excited only by external action on the platform. The behavior of the platform under external loading is examined. Lavrent'ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 173–181, January–February, 2000.     

On positive periodic solutions of nonlinear impulsive functional differential equations

Using the Krasnosel’skii theorem on a fixed point of a mapping in a cone, we obtain conditions for the existence of positive, piecewise-smooth, periodic solutions of impulsive functional differential equations. Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 501–511, October–December, 2008.     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.     

Experimental study of density fluctuations in a hypersonic laminar wake behind a cone

The characteristics of natural fluctuations of density in a laminar near wake behind a sharp cone in a hypersonic flow of nitrogen at zero incidence are studied by the method of electronbeam fluorescence at Mach numberM=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹. The distributions of the mean density, integral fluctuations, and spectra of density fluctuations are obtained, the longitudinal and azimuthal phase velocities of perturbations are determined, and the growth rates of perturbations in the wake are found. The results are compared with the measurement data in the shock layer on a flat plate. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 111–117, May–June, 2000     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.