Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Control of a reservoir partially filled with liquid based on Gauss\u27s principle of least constraint (deceleration task)
Get PDFThe task of constructing control for the motion of a given reservoir - a liquid with a free surface mechanical system is provided in the presence of constant perturbations - the oscillations of the free surface of the liquid. To construct the control, the principle of the least coaxing of Gauss was used, which allows to minimize the control load and implement the given laws of the software movement. The control calculation was carried out on the basis of a simplified linear model with two degrees of freedom, which allowed the control function to be obtained in analytical form for various software laws (including nonlinear) movement of the reservoir and free surface of the liquid. The tank partially filled with a liquid, which initially moves evenly at a given speed, must be completely stopped at a given time. The control, constructed for the implementation of linear software laws of motion, can be used only to provide "comfortable" movements of the reservoir, that is, in the absence of large disturbances of the free surface of the liquid. In order to ensure the movement of the reservoir in the presence of highly intense loads, it is necessary to introduce nonlinear software motion laws for obtaining and using a nonlinear control law.Key words: Gauss’s principle, program movement.Pages of the article in the issue: 86-89Language of the article: Ukrainia
Stochastic permanence of solution to stochastic non-autonomous logistic equation with jumps
Get PDFIt is investigated the non-autonomous logistic differential equation with disturbance of coeffcients by white noise, centered and non-centered Poisson noises. The coeffcients of equation are locally Lipschitz continuous but do not satisfy the linear growth condition. This equation describes the dynamics of population in the Verhulst model which takes into account the logistic eect: an increase of the population size produces a fertility decrease and a mortality increase; since resources are limited, if the population size exceeds some threshold level, the habitat cannot support the growth. The property of stochastic permanence is desirable since it means the long time survival in a population dynamics. The suffcient conditions for the stochastic permanence of population in the considered model is obtained.Key words: stochastic permanence, non-autonomous logistic dierential equation, stochastic differential equation, centered and non-centered Poisson measures.Pages of the article in the issue: 10-13Language of the article: UkrainianIt is investigated the non-autonomous logistic dierential equation with disturbance of coeffcients by white noise, centered and non-centered Poisson noises. The coeffcients of equation are locally Lipschitz continuous but do not satisfy the linear growth condition. This equation describes the dynamics of population in the Verhulst model which takes into account the logistic eect: an increase of the population size produces a fertility decrease and a mortality increase; since resources are limited, if the population size exceeds some threshold level, the habitat cannot support the growth. The property of stochastic permanence is desirable since it means the long time survival in a population dynamics. The suffcient conditions for the stochastic permanence of population in the considered model is obtained.Key words: stochastic permanence, non-autonomous logistic differential equation, stochastic differential equation, centered and non-centered Poisson measures.Pages of the article in the issue: 10 - 13Language of the article: Ukrainia
Thermal instability of nanocomposite structural elements under cyclic loading
Get PDFThe failure of nanocomposite structural elements due to the self-heatingunder harmonic loading is investigated. The technique of the nanocomposite structural element life prediction is elaborated with accounting for the influence of dissipative heating and volume fraction of nanofibers on mechanical stability of polymeric nanocomposite rod subjected to both static and monoharmonic loading that are based on the concept of temperature and amplitude dependent complex moduli. In this regard, special modified homogenization procedure based on the Mori-Tanaka method is designed with taking into account the effects of interface on response of nanocomposite material to derive the complex moduli for the nanocomposite with either random or unidirectional orientation of nanofibers.Complex moduli approach is used to formulate the approximate (single frequency approximation) problem statement. The problem is solved numerically. Influence of carbon nanotube fiber volume fraction on the high cycle fatigue behavior for the nanocomposite rod with both randomly and unidirectionally oriented nanofibers is estimated. It is found that volume fraction of nanofibers affects significantly the temperature level and, thus, fatigue life of nanocomposite element. The approach presented in this paper can be useful to understanding of the cyclic behavior of viscoelastic structures and investigations of the fatigue with taking into account the vibro-heating effect due to the mechanical energy dissipation.Key words: nanocomposite, thermal instability, dissipative heating.Pages of the article in the issue: 46-49Language of the article: Ukrainia
The stress state in an elastic body with a rigid inclusion of the shape of three segments broken line under the action of the harmonic oscillation of the longitudinal shift
Get PDFThere is a thin absolutely rigid inclusion that in a cross-section represents three segments broken line in an infinite elastic medium (matrix) that is in the conditions of antiplane strain. The inclusion is under the action of harmonic shear force Pe^{iwt} along the axis Oz. Under the conditions of the antiplane strain the only one different from 0 z-component of displacement vector W (x; y) satisfies the Helmholtz equation. The inclusion is fully couple with the matrix. The tangential stresses are discontinuous on the inclusion with unknown jumps.The method of the solution is based on the representation of displacement W (x; y) by discontinuous solutions of the Helmholtz equation. After the satisfaction of the conditions on the inclusion the system of integral equations relatively unknown jumps is obtained. One of the main results is a numerical method for solving the obtained system, which takes into account the singularity of the solution and is based on the use of the special quadrature formulas for singular integrals.Key words: inclusion, shear force, fixed singularities.Pages of the article in the issue: 158-161Language of the article: Ukrainia
To the problem of influence of the third invariant of stress deviator on the process of longterm deformation of nonlinear viscoelastic materials
Get PDFThe problem on the influence of stressed state on the process of long-term deformation of nonlinear viscoelastic materials under the simple and quasi-simple modes of loading by introduction of the function with the parameter of Lode angle into the defining equations is considered. The mentioned function is determined by analysis of base experimental data obtained from the base experiments on axial tension and pure torsion. Physical and mechanical properties of nonlinear viscoelastic solids are defined by the correspondence between the invariants of deformation tensors and tensions according to the modified nonlinear Rabotnov’s model for viscoelasticity. The heredity kernels are given by the fractional-exponential function. The constructed defining equations are verified experimentally for the problems of determination of nonlinear creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density and low pressure polyethylene. As a result of juxtaposition of experimental data and calculations it is a stated that allowing for the type of stressed state improves their agreement qualitatively and quantitatively.Key words: nonlinear viscoelastic materials, tension with torsion, creep strains, Lode angle.Pages of the article in the issue: 186-189Language of the article: Ukrainia
Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities
Get PDFThe flow of viscous incompressible fluid in a cylindrical duct with two serial diaphragms is studied by the numerical solution of the unsteady Navier–Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is nonstationary and is characterized by the presence of an unstable shear layer under certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity and pressure fields in the orifice of the second diaphragm. There can be four self-sustained oscillation modes depending on the length of the cavity formed by the diaphragms. With the increase in the distance between the diaphragms, the frequency of oscillations decreases within the same self-oscillation mode and rises sharply with the switch to the next mode.Key words: direct numerical simulation, cylindrical cavity, duct with diaphragms, vortical structures, self-sustained oscillations.Pages of the article in the issue: 218-221Language of the article: Ukrainia
Estimation of distribution of suprema of a strictly ?-sub-Gaussian quasi shot noise process
Get PDFIn this paper, there are studied properties of a strictly ?-sub-Gaussian quasi shot noise process X(t) = integral_{-?}^{+?} g(t, u) d?(u), t ? R, generated by the process ? and the response function g. New estimates for distributions of suprema of such processes are derived. An example of application of the obtained results is given.Key words: shot noise processes, distrubution of suprema of a process, ?-sub-Gaussian processes.Pages of the article in the issue: 8 - 17Language of the article: Ukrainia
Finite element analysis of elastic-plastic state of crack at the interface between infinite plane and circular inclusion
Get PDFThe problem on determining of elastic-plastic stress-strain state of infinite plane with a circular inclusion made from another material and an arc crack at the interface under action of arbitrary mechanical loadings applied at infinity is considered using the FEM approach. The problem is resolved within the framework of contact model for which the possibility of appearance of contact macrozones between crack faces is assumed. The isotropic hardening of materials with bilinear approximation of stress-strain curves is considered. The infinite plane is modeled by square domain whose size is of an order of magnitude greater than inclusion diameter. Contact interaction of crack faces is simulated using gap elements. To obtain the energy release rate the J-integrals are calculated along several closed contours around the crack tips. The comparison of obtained results with available analytical solutions for linear elasticity shows that insignificant differences take place during transformation from pure elastic to elastic-plastic stress-strain state.Key words: arc crack, elastic-plastic state, finite element method, contact problem.Pages of the article in the issue: 20-23Language of the article: Ukrainia
Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface
Get PDFAcoustic radiation force effect on a liquid spherical drop placed in the vicinity of an ideal liquid free surface is studied. The problem of determination of the radiation forces acting on an obstacle in ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on a spherical drop of ideal liquid placed in turn in a liquid by its free plane surface is studied here for the case of the incident plane sound wave propagating perpendicularly to the liquid boundary. As a result, the liquid sphere is appeared to be located in the standing sound wave of pressure which has its displacement node at the free surface. Problem solution is obtained as a three step procedure. Initially, solution of the problem of an incident wave scattering at the drop is derived. With making use of the results obtained, the second step encompasses determining of hydrodynamic forces acting on the liquid spherical drop with their subsequent averaging over the suitable time interval at the third step. It is found there frequencies of the incident wave exist that provide zero radiation force acting on the drop which is immobile in this case. These equilibrium positions of the spherical drop could be stable or unstable with respect to the incident wave frequency variation.Key words: ideal liquid, plane acoustic wave, liquid spherical particle, hydrodynamic force, radiation force.Pages of the article in the issue: 50-53Language of the article: Ukrainia
Thermoelastic behavior of a bimaterial with interface crack filled with an incompressible fluid
Get PDFThermo-stressed state of the bimaterial with the interfacial crack filled with an incompressible fluid is investigated. The bimaterial with zero Dundurs parameter is considered. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for a temperature jump between the cracks faces and an opening crack. The pressure of the fluid is determined from the equation of the incompressible fluid. Using the method of successive approximations a numerical solution of the problem is constructed. The opening crack and temperature jump are determined by the finite sum for Chebyshev polynomials of the second kind. The coefficients for Chebyshev polynomials are determined from the system of linear algebraic equations. Having made numerical calculations, the dependences of the pressure of the fluid and the opening crack from the mechanical loads and density and direction of the heat flow have been constructed. The influence of fluid pressure on the stress intensity factor mode I are analyzed.Key words: bimaterial, interfacial crack, incompressible fluid, fluid pressure.Pages of the article in the issue: 206-209Language of the article: Ukrainia