Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Features of the method of partial domains
Get PDFPartial domains method is used effectively to study the problems of the radiation and dissipation of the waves of different nature. The main results of this method are relevant to the cases when adjacent domains do not intersect (it means that they have only one common border). If the adjacent partial domains intersect (it means that they can have two common borders) the traditional way of using partial domains method can be ineffective. An improved way of using partial domains method in the cases when adjacent domains intersect is described in the article. The article shows that one of the following conditions can be set on each of the borders of intersection region: functions equality on both sides of the border or equality of the normal derivative functions. The peculiarity of this approach is that the wave number in the problem should not be the same as the wave number of the partial domains intersection. However, the indicated restriction is not an obstacle to the application of this approach.Key words: partial domains, waveguide.Pages of the article in the issue: 38-41Language of the article: Ukrainia
Large elastic-plastic deformation of square membranes subjected to localised pulse pressure loads
Get PDFDuctile isotropic materials are widely used in protective systems against transient pulse pressure loads, such as those of localised blasts. This is due to the combined elastic-plastic response which contributes to dissipation of total impulse from extensive loading as the energy stored elastically limits deformation while the energy expended plastically limits the level of transferred forces in the structure. In the case of thin, modern armour graded steel plates, the tailored metallurgy helps the structure store energy within the bounds of elastic region, which may be dissipated at a later stage as damping kills it off in subsequent cycles. On the other hand, the plastic work is almost entirely converted to heat and dissipates.The present work focuses on the elastic and plastic energies in the membrane and aims at deducing, from the minimization of Föppl-Von-Kármán (FVK) energy functional combined with enforcing the constitutive relations of limit analysis, the dynamic elastic-plastic response of localised blast loaded square membranes undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various temporal shapes (e.g. rectangular, linear, exponential).Considering the elastic response, a single-degree-of-freedom model was developed from the prescribed displacement field and associated stress tensor having clamped and simply supported boundary conditions. The explicit closed form solutions were sought by using the Ritz-Galerkin’s variational method as well as the Poincaré-Lindstedt perturbation method. The theoretical solutions of rigid-perfectly plastic square membranes subjected to the same blast scenarios were then discussed. From the combined effects we deduce the load displacement curves representing the trajectory of the nonlinear elastic-perfectly plastic structure.Key words: localised blast, square membrane, Ritz-Galerkin method.Pages of the article in the issue: 126-133Language of the article: Englis
Resonant steady-state sloshing in upright tanks performing a three-dimensional periodic motion
Get PDFAnalytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary problems for special systems of ordinary differential equations. Their solutions describe capillary curves, which appear as intersections of the capillary menisci and (depending on the container type) either crosssection or meridional plane. Further studies on capillary waves require to know analytical approximations of these capillary curves in the Cn, n ? 3 metrics. An objective may consists of constructing analytical approximate solutions of the corresponding systems of ordinary differential equations. The present paper focuses on limits of applicability of the Taylorpolynomial and Pad´e approximations, which were proposed for this class of capillary problems in 1984 by Barnyak&Timokha.Key words: sloshing, damping, steady-state waves.Pages of the article in the issue: 214-217Language of the article: Englis
Cardiorespiratory system as system with limited excitation
Get PDFA new modified cardiorespiratory model based on the famous DeBoer beat-to-beat model and Zaslavsky map (which describes dynamics of the respiratory system as a generator of central type) was studied in details. In this case the respiratory tract was firstly modeled by a self-oscillating system under the impulsive influence of heartbeat and cardiovascular system was represented as an oscillating system with a limited excitation. The steady-state regimes of the model are investigated by methods of the dynamical system theory. Firstly, the chaotic regimes were found out. The dynamics of heartbeat and respiratory systems are in good correspondence with experimental information of healthy man. The found out irregularities of phase trajectories of the modified model depend on intensity of influence of heart rhythm on breathing, what is well known characteristic for the dynamics of the cardiovascular system of healthy man.Key words: cardiovascular system, respiratory system, limited excitation, chaos.Pages of the article in the issue: 60 - 63Language of the article: Ukrainia
Basic Characteristics and Industrial Application of Styrene Copolymer-Based Thermoplastic Elastomers (Overview)
No full textThermoplastic elastomers (TPEs) have elastic properties that are similar to rubber but capable of melting and all thermoplastic properties. Block copolymers are also widely used, in which there are links of different polymers in the structure of their macromolecules. So styrene-ethylene-butylene- styrene (SEBS) belongs to the second generation, the products of which have high physical and mechanical properties, and biocompatibility allows it to be used in the medical field. The main characteristics and analysis of advantages of TPE on the example of SBSS in comparison with traditional materials are presented in the paper.Key words: thermoplastic elastomers, SEBS, structure, properties, application.Pages of the article in the issue: 98 - 103Language of the article: Ukrainia
Exfoliation the flexible continuous reinforcements of the free edge of a semiinfinite plate
Get PDFExfoliation the not extensible flexible stiffener heated up to the set temperature is investigated in conditions of a plane problem thermoelasticity. The flexible stiffener is placed at edge of the semi-infinite plates in conditions ideal thermal contact and action the stretching loading on the plate. Development of localized zones of prefracture (the weakened contact) is precede to separation the stiffener in vicinities of her ends. They can correspond to regions of damages, plastic deformation, partial break of connection and another precedes. On area outside of zones of prefracture the perfect mechanical contact is remaining. The analytical decision of a problem is shown to problem Koshy for differential equation of the first order and realized its numerical analysis. Physically correct limited stresses and deformations are received in all points of a composition. Tangents stresses also satisfy to relationship of pair law. Basic part of loading from reinforcements to plate is transfer in neighbourhood of reinforcement ends. Interference of power and temperature loadings on flexible stiffener separation is investigated.Key words: reinforcement, exfoliation, plane problem, zone of prefracture.Pages of the article in the issue: 94-97Language of the article: Ukrainia
Method of finite bodies for determination of the plane stressed state of rectangular plates with a rectangular hole
Get PDFThe paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.Key words: plate, rectangular hole, method finite bodies.Pages of the article in the issue: 170-173Language of the article: Ukrainia
Semantic Analysis of Texts Presented in Natural Language
Get PDFThe article considers a cognitive approach to one of the problems of artificial intelligence consisting in semantic analysis of texts presented in natural language. Development of methods and means of discourse analysis is a necessary step for building systems of intellectual communication between a person and a computer (robot). A scientific hypothesis is proposed suggesting that an observer of the environment studies and understands the World when he is able to highlight and analyze Facts, Events and Situations. Corresponding linguistic and cognitive structures of these "units of semantic analysis" of the reality - "Fact", "Event", "Situation" and "Sense" - are proposed and justified. The Sense is considered a prerequisite for understanding dialogue and discourse.Key words: artificial intelligence, cognitive science, knowledge, sense, understanding.Pages of the article in the issue: 228-233Language of the article: Ukrainia
Approximate method of solving one periodic optimal regulated boundary value problem
No full textIn the present work we considered the solution of one periodic optimal regulated boundary value problem by the asymptotic method. For the solution of the problem with extended functional writing, boundary conditions and Euler-Lagrange equations were found. The approach to the solution of the problem depending on a small parameter by seeking a system of nonlinear differential equations and solving Euler-Lagrange equations, the solution of the general problem in the first approach comes down to solving two nonlinear algebraic equations.Key words: optimal regulation, asymptotic method, periodic condition.Pages of the article in the issue: 66 - 69Language of the article: EnglishIn the present work we considered the solution of one periodic optimal regulated boundary value problem by the asymptotic method. For the solution of the problem with extended functional writing, boundary conditions and Euler-Lagrange equations were found. The approach to the solution of the problem depending on a small parameter by seeking a system of nonlinear differential equations and solving Euler-Lagrange equations, the solution of the general problem in the first approach comes down to solving two nonlinear algebraic equations.Key words: optimal regulation, asymptotic method, periodic condition.Pages of the article in the issue: 66 - 69Language of the article: Englis
Formulation of the problem of thermomechanics for a flexible cylindrical shell with piezoactive layers with taking into account to displacements
Get PDFThe formulation of problem on the forced resonant vibration and dissipative heating of layered element of structure containing both piezoelectric and electrically passive layers is considered. The improved problem statement taking account of both shear strain and rotatory inertia as well as geometrical nonlinearity is developed. Particular statement of the problem of axisymmetric vibration and dissipative heating of three layer cylidrical shell is formulated. It is assumed that the core layer of the shell is composed of the electrically passive material while the outer layers are manufactured from the piezoceramics. Theory of coupled thermo-electro-viscoelasticity is used to derive the problem statement in the case of monoharmonic loading. Within this theory, the concept of complex-value modulae is applied to formulate the relations between main field characteristics. It is also supposed that the piezo-active material characteristics do not depend on the temperature. Then the coupled problem is reduced to the problem of mechanics on the forced nonlinear vibrations and dissipative heating of the layered plate. Complete set of complex analogs of motion equations, geometric equations and constitutive relations was used to derive the resolving system of equations. Numerical method to attack this nonlinear system of ordinary differential equations supplemented with necessary boundary conditions is developed.Key words: cylindrical shell,resonated vibration, dissipative heating, piezoelectric sensors.Pages of the article in the issue: 78-81Language of the article: Ukrainia