Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Steady-state sloshing in an orbitally-forced square-base tank
Get PDFThe paper conducts a series of analytical studies on the resonant steady-state sloshing in a rigid square base container, which have been originated by Faltinsen & Timokha who derived and applied the Narimanov-Moiseev—type nonlinear modal equations for investigation in the sloshing problem. The modal equations, which consist on nine-dimensional system of ordinary differential equations, should be applicable for sway/pitch/surge/roll periodic excitations but, due to, basically, mathematical difficulties, the previous papers exclusively concentrated on the reciprocating (longitudinal, oblique and diagonal) motions of the container. This article is showed that the steady-state waves caused by this kind of forcing are asymptotically identical to those occurring when the tank performs horizontal orbital motions. We generalize the previous results by Faltinsen & Timokha to classify the steady-state wave regimes versus the semi-axes ratio of the forcing ellipse in the tank which is filled by a liquid with a finite depth.Key words: sloshing, damping, steady-state waves.Pages of the article in the issue: 210-213Language of the article: Englis
On asymptotic distribution of Koenker-Bassett estimator of the parameter of linear regression model with strongly dependent noise
Get PDFAsymptotic properties of Koenker - Bassett estimators of linear regression model parameters with discrete observation time and random noise being nonlinear local transformation of Gaussian stationary time series with singular spectrum are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise, under which the Koenker - Bassett estimators of regression model parameters are asymptotically normal. Linear regression model with discrete observation time and bounded open convex parametric set is the object of the studying. Asymptotic normality of unknown parameters Koenker - Bassett estimators are obtained. For getting these results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev - Hermite polynomials of the transformed Gaussian time series values and it‘s covariances, central limit theorem for weighted sums of the values of such a local transformation.Key words: linear regression model, regression function, local transformation of Gaussian stationary time series, Koenker - Bassett estimators, asymptotic normality.Pages of the article in the issue: 18 - 35Language of the article: Ukrainia
Influence of the material anisotropy on the limit state of orthotropic plate with periodic system of collinear cracks under biaxial loading
Get PDFIn the presented paper, the limiting state of the orthotropic plates weakened by the periodic system of collinear cracks under biaxial external loading is studied on the basis of the modified crack model of the Leonov-Panasyuk-Dagdale. The material of plate satisfies the strength condition of the general form. On the basis of the solution of a similar problem for an orthotropic plate with one crack, we obtain the relations for determining the basic parameters of a crack model, such as the size of the process zones, the stresses in these zones, and the opening at the top of the cracks. The criterion of critical crack opening is selected as a fracture criterion. On the example of a material satisfying Hoffman strength criterion (generalization of the Mises–Hill criterion, which takes into account the dependence of the difference between the tensile and compressive strength of unidirectional composite materials), the fracture mechanism of a plate weakened by the periodic system of collinear cracks was investigated. The influence of the degree of material anisotropy and biaxiality of external loading on the fracture process and the limiting state of the plate are shown.Key words: periodic system of cracks, biaxial loading, orthotropy.Pages of the article in the issue: 34-37Language of the article: Englis
Towards the solution of creep problems of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials
Get PDFA new approach to the creep strains analysis of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials under combined loading with uniaxial tension and torsion has been proposed. The system of equations that is constructed according to the deviators proportionality hypothesis has been chosen as the creep constitutive equations the nonlinearity of viscoelastic properties in which is given with respect to the creep strain intensity and volumetric strain by the Rabotnov type models. The kernels of creep strain intensity and volumetric strain are given by the relations that establish the relationships between these kernels and one-dimensional creep kernels determined from a system of base experiments. One-dimensional tension with the measurement of longitudinal and transverse strains as well as one-dimensional tension and pure torsion with the measurement of longitudinal and shearing strains have been considered as base experiments. The functions of nonlinearity of viscoelastic properties are given by smoothing cubic splines. The problems of the analysis of longitudinal, transverse and shearing strains of thin-shelled tubular specimens made of “high density polyethylene PEHD” have been solved and experimentally approved.Key words: nonlinear viscoelastisity, biaxial stress state, creep process.Pages of the article in the issue: 42-45Language of the article: Ukrainia
Application of the finite element-differences method for modeling of filtration processes
Get PDFWe consider modeling and geophysical interpretation of the obtained results in the oil and gas production problems. For solving these practical problems, we use combined finite element-differences method of resolving piezoconductivity problem with calculation of heterogeneous filtration parameters distribution of oil and gas productive reservoirs and oil-gas penetration conditions in the borders of the reservoirs. At that, we consider the main factors, which influence on the intensity of filtration processes near oil production well and gas production well respectively. These factors are important for effective supporting in practice high level of the oil and gas production. On the base of computer modeling, we have showed that intensity of filtration process near the acting oil and gas production wells mainly depends on oil phase and respectively gas phase permeability, as in close zone of well acting so in remote zone. The viscosity and reservoir porosity parameters in close and remote zones of the well action have little direct effect on filtration process near the acting well. However, these parameters can influence on the filtration process implicitly via direct acting on the respective phase permeability. We also have carried out analysis of the pumping well influence on the filtration process near production well in different practical cases.Key words: computer modeling, oil and gas producing, combined finite element-differences method.Pages of the article in the issue: 114-117Language of the article: Ukrainia
Consideration of wear in plane contact of rectangular punch and elastic half-plane
Get PDFThe plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.Key words: contact, friction, wear.Pages of the article in the issue: 138-141Language of the article: Ukrainia
Creep of isotropic homogeneous and nonaging of linear-viscoelastic materials under the complex stress state
Get PDFThe relaxation of isotropic homogeneous and non-aging linear-viscoelastic materials under conditions of complex stress state is considered. Thin-walled tubular specimens of High Density Polyethylene (HDPE) for creep under a single-axial stretching, with a pure twist and combined load tension and torsion are considered as base experiments, tests. The solution is obtained by generalizing the initial one-dimensional viscoelasticity model to a complex stressed state, constructed using the hypothesis of the proportionality of deviators. The heredity kernels are given by the Rabotnov’s fractional-exponential function. The dependence between the kernels of intensity and volumetric creep is established, which determine the scalar properties of linear viscoelastic materials in the conditions of a complex stressed state in the defining equations of the type of equations of small elastic-plastic deformations, and the kernels of longitudinal and transverse creep defining the hereditary properties of linear-viscoelastic materials under the conditions of the uniaxial tension. The problems of stress relaxation calculation of thin walled tubes under combined tension with torsion have been solved and experimentally approved.Key words: relaxation, linear-viscoelastic, heredity kernel.Pages of the article in the issue: 150-153Language of the article: Ukrainia
Determination of quasi-static thermoelastic state of layered thermosensitive plates
Get PDFThe technique of determining the quasistatic thermoelastic state of the layered thermosensitive plates free of load is illustrated. Much attention is paid to finding analytical-numerical solutions of one-dimensional non-stationary heat conduction problems taking into account the temperature dependences of the thermal and temperature conductivity coefficients. Their finding involves use of the Kirchhoff transformation, generalized functions, Green\u27s functions of the corresponding linear heat conduction problem, exact sums of the series, in particular those for which the Gibbs effect takes place, linear splines and solving the received recurrent systems of nonlinear algebraic equations relative to the values in the nodes of the spline of the Kirchhoff variable on the layer division surfaces and the derivative in time on inner flat-parallel surfaces of layers. The results of numerical calculations of temperature fields in two-layer plates with different thicknesses of layers and the external surface heated by a constant heat flux are presented. The accuracy of the found solution is investigated. The comparison of the temperature fields, which are determined assuming simple nonlinearity, stable thermophysical characteristics with the ones based on the exact solution of the corresponding nonlinear stationary heat conduction problem is fulfilled.Key words: layered thermosensitive plate, thermoelastic state, nonlinear heat conduction problem, Green\u27s function, linear splines.Pages of the article in the issue: 162-165Language of the article: Ukrainia
About general solutions of Euler’s and Navier-Stokes equations
Get PDFConstructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler\u27s and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.Key words: Euler’s and Navier-Stokes equations, general solutions.Pages of the article in the issue: 190-193Language of the article: Ukrainia
Model of blood flow along the arterial bed, taking into account the bioactivity of the vessel wall
No full textThe modification of a two-dimensional model of incompressible viscous fluid motion along a deformed thick-walled tube from viscoelastic bioactive material is proposed in connection to the modeling of blood flow along the arterial bed is proposed. The motion of a viscous incompressible fluid is described by a system of equations including the Navier-Stokes equations and the continuity equation. The behavior of the tube wall material is described by a 5-element rheological model with one active element. The solution of the problem is solved setting boundary conditions on the interface of the two media, the outer surface of the tube is considered as non-moving. At the end of the tube, a zero-dimensional Frank model with regulation is considered, as a model of the microcirculatory bed. The dispersion equation for the propagation of wave velocity is obtained for the case of active properties of tube, the amplitudes of fluid velocities, wall displacements, and fluid and tube pressures. Numerical computations have been carried out for the model parameters corresponded to the normal and pathological arterial wall.Key words: the model of arterial bed, pulse waves, wave dispersion, active material.Pages of the article in the issue: 88 - 92Language of the article: Ukrainia