The paper investigates the static state of a space elevator that is a platform held in a circular orbit by a stretched elastic cable in a spherically symmetric field of gravitational-centrifugal forces. To select rational mass and orbital parameters of the system, two variants of the cable in the approximation of a heavy elastic thread are considered, namely, a homogeneous cable and a uniform-strength cable. The relations between the mass of the platform, the radius of its orbit, and the characteristics of the cable are obtained, which provide its strength and tension necessary for operation of the lift “delivering” the output satellites in their orbits.

Разработана нелинейная двухмодовая модель самовозбуждения вертикально- крутильных колебаний провода в ветровом потоке при наличии гололедных отложений. Самовозбуждение колебаний трактуется как неустойчивость равновесного состояния вследствие возникновения поперечной аэродинамической силы при закручивании провода (эффект Магнуса) и динамической связи вертикальных и крутильных колебаний. Провод рассматривается как тяжелая гибкая нить с осредненными характеристиками, закреплённая между двумя равновысокими опорами. Натяжение провода считается постоянным по длине, но переменным во времени. Статические и динамические компоненты полных деформаций растяжения записываются в квадратичном приближении. Формы вертикальных и крутильных колебаний относительно статического положения равновесия аппроксимируются квадратичной функцией, близкой к первым парциальным модам. Уравнения колебаний провода записываются в форме уравнений Лагранжа 2-го рода. Обобщенными координатами, отсчитываемыми от положений статического равновесия, являются изменения стрелы провисания и угла поворота сечения провода в центре пролета. Определена группа критериальных безразмерных параметров модели и на основе данных о технических характеристиках проводов высоковольтных линий электропередачи выявлены практические диапазоны их изменения. На основе линеаризованных уравнений получены условия самовозбуждения колебаний в виде зависимости критического параметра скорости ветра от параметра, обобщенно характеризующего возможные инерционные и геометрические характеристики гололедных отложений.

The paper describes a new device that allows us to study the effect of ultraviolet irradiation on the electrorheological characteristics of new photosensitive materials based on colloidal polyimide systems containing SO3H (PI-I) and SO3Na (PI-II) groups. The samples were analyzed using rotational viscometry methods, and a significant effect of irradiation of the systems on the flow velocity and hence the viscosity of the medium and the electrorheological response was shown. At the same time, the dimensional and microrheological properties of colloidal polyimide systems in polar and nonpolar media under simultaneous ultraviolet irradiation and exposure to an electric field were monitored using IR spectroscopy and dynamic light scattering methods. The mobility and zeta potential of polyimide molecules were determined using a sensitive method of phase analysis of light scattering. It is shown that in almost all cases, irradiation of colloidal systems of polyimides led to the uncontrolled formation of larger particles, which decreased during the thermal reaction almost to the initial size, which indicates the stability of the studied systems to external influences (irradiation and electric current).

Рассматривается система из двух проводов, связанных дистанционными распорками в виде жестких стержней. На провода воздействует ветровой поток так, что один провод находится в аэродинамическом (спутном) следе другого, что приводит к возникновению автоколебательного процесса. Следовая связь между проводами моделируется с помощью модифицированной теории Симпсона с использованием эмпирических данных Блевинса и Прайса. Дифференциальные уравнения колебаний выводятся на основе принципа возможных перемещений в обобщенных координатах с учётом нелинейностей упругих и инерционных сил, а также аэродинамических сил в спутном следе. Для дискретизации по пространственным координатам используется метод конечных элементов с выбором линейных и тригонометрических функций формы в качестве базисных. Сила натяжения и продольная деформация провода считается в пределах элемента постоянными величинами. Зависимость деформации от поперечных перемещений определяется квадратичным приближением. Для получения конечных выражений для аэродинамических сил используются полиномиальные аппроксимации экспериментальных данных, а также линеаризация выражений для этих сил, записанных в локальных (элементных) координатах.

Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of “tracking” type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells.

The efficiency of electric-pulse disintegration of the scrap of synthetic corundum abrasive wheels is studied under laboratory conditions. At the chosen parameters of selective destruction of the abrasive scrap, the degree of separation of synthetic corundum grains, the size of which practically corresponds to the size of the initial fraction, is more than 50%.

In laboratory conditions the efficiency of electropulse disintegration of scrap abrasive wheels made of electrocorundum has been investigated. It is shown that at the chosen parameters of the process of selective destruction of abrasive scrap, the separation degree of electrocorundum grains, coarseness of which almost corresponds to the initial fraction, is more than 50%.

Considering finite element approach applied to modelling of wind-induced split-phase overhead power line conductor oscillations caused by aerodynamic wake. Model represents an aeroelastic system including twin bundled conductor with spacers. Modified Simpson’s theory is used for conductor wake coupling simulation. Assuming small oscillating conductor deflection from element ends connection line compared to element length, thus the element tension and element tensile strain can be considered as constant values. Strain, as function of transverse displacements, defines as quadratic approximation. Element absolute displacements and twisting angles, together with Ritz’s method coefficients is taken as generalized coordinates, in which conductor move equations are compiled with non-linear elastic, inertial and aerodynamic forces. Appropriate linearized small oscillation equations near the static equilibrium are derived – those can be used for defining system flutter critical wind velocity. An example with split-phase twin bundled conductor, three-sub-span system is presented.

Математическая модель субколебаний формулируется на основе метода конечных элементов. В качестве обобщенных координат принимаются абсолютные перемещения и углы закручивания узловых сечений, а также коэффициенты тригонометрических разложений, описывающих локальные (внутренние) степени свободы в пределах каждого элемента. Для определения аэродинамических сил используются полиномиальные аппроксимации экспериментальных данных Блевинса и Прайса. Деформация растяжения записывается в квадратичном приближении. Для численного интегрирования системы уравнений колебаний используется неявный алгоритм, основанный на параметризации уравнений с выбором в качестве аргумента длины интегральной кривой решения. Рассмотрены задачи о колебаниях двух проводов, связанных распорками.

Исследуется несущая способность спиральных зажимов, которые монтируются на проводах (тросах) для их натяжения, соединения, ремонта и пр. Конструкция спиральных зажимов образуется из растянутых спиралей, навиваемых на провода с натягом, что позволяет получать соединения при растяжении практически неразъемными. Формулируется общая задача о взаимодействии спиральных зажимов с повивами (проволочными слоями) провода. Даются разнообразные асимптотические решения начальных и краевых задач, и определяются конструктивные параметры зажимов, обеспечивающие их несущую способность. Каждый повив представляется с позиции энергетического подхода как эквивалентная по упругим свойствам анизотропная цилиндрическая оболочка, а проволочная конструкция в целом рассматривается как система вложенных друг в друга цилиндрических оболочек, взаимодействующих сил давления и трения. Эквивалентность упругих свойств оболочки свойствам повива устанавливается с использованием энергетического осреднения. Определяющие соотношения, полученные с использованием теоремы Кастильяно, связывают обобщенные перемещения и соответствующие им силы. Матрица в этих соотношениях представляет собой матрицу жесткости или матрицу податливости спиральной проволочной конструкции. Такая постановка позволяет решать с единых позиций разнообразные задачи взаимодействия спиральных зажимов с повивами провода и исследовать механизм передачи усилия с зажимов на провод. Из условия равновесия элементарного кольца оболочки записываются уравнения статики. Считается, что длина зажима настолько велика, что взаимовлиянием его концов можно пренебречь, т.е. зажим рассматривается как полубесконечная оболочка. Такая модель позволяется ставить различные начальные и краевые задачи в зависимости от краевых условий и способов монтажа на проводе.

The bearing capacity of spiral clamps, which are mounted on wires (cables) for their tension, connection, repair, etc., is studied. The design of spiral clamps is formed from stretched spirals that are wound onto conductors with an interference fit, which makes it possible to obtain tensile connections practically inseparable. The general problem of the interaction of spiral clamps and overhead line conductor layers is formulated. Different asymptotic solutions are given for initial and boundary value problems, and the design parameters of spiral clamps are determined to provide their carrying capacity. A wire layer is represented by the energy approach as an equivalent anisotropic elastic cylindrical shell, and wire construction as a whole is considered as a system of cylindrical shells inserted each other and interacting by forces of pressure and friction. The equivalence of the elastic properties of the shell to the properties of the wire layer is established using energy averaging. The constitutive relations obtained using the Castigliano theorem relate the generalized displacements and the corresponding forces. The matrix in these ratios is a stiffness matrix or flexibility matrix of a spiral wire structure. Such approach allows variety of interaction problems for spiral clamps with conductor layers to be solved, and the force transfer mechanism to be investigated from common positions. Static equations are written from the equilibrium of the elementary shell ring. It is considered that the length of the clamp is so great that the mutual influence of its ends can be neglected; the clamp is modeled as semi-infinite shell. This model allows the different initial and boundary value problems to be formulated, depending on the boundary conditions and clamp mounting methods on a conductor.

Analysis of overhead power transmission lines (OPL) involves the simulation of statics and oscillation. Solving such problems strictly requires the proper accounting of the internal conductor structure, in particular for power safety and reliability systems of information-telecommunication supply of aerodromes and aircraft systems, as well as for overhead transmission lines subjected to intense wind, especially in icing conditions. Due to the complexity of wire structures, known issues arise in the estimates of their deformations, stiffness, bearing capacity, etc. For instance, the bending stiffness of the conductor can vary considerably. Consequently, the stiffness can vary along the conductor axis as well as in time. This paper proposes a new deformation model of wire structures similar to typical OPL conductors. Such structures include not only conductors and cables, but spiral clamps intended for tension, suspension, joining, protection, and repair of conductors. Based on energy averaging each wire layer is considered as an equivalent elastic anisotropic cylindrical shell. Therefore a conductor or a spiral clamp can be modeled as a system of shells nested into each other and interacting by means of pressure and friction forces. In the process of the study, calculations were made that made it possible to formulate equations for the matrices of flexibility and cruelty of spiral structures. The interaction problem for a tension clamp with an external wire layer of a conductor has been formulated and solved. Finally, the mechanism of the force transfer from the clamp on the conductor has been investigated.

The interaction of a spiral wire clamp and a line conductor (cable, rope) is considered to estimate the bearing capacity of the wire clamp and to determine its structural and technological properties. The corresponding boundary and initial value problems are formulated to compute the structural properties of multilayer tension and connecting spiral clamps of various finite lengths. The paper presents an algorithm for estimating the bearing capacity of the connecting clamp with conducting aluminum layer and external protective steel wire layer.

В работе приводятся результаты численного моделирования пляски (галопирования) проводов воздушных ЛЭП с маятниковыми гасителями с целью анализа эффективности их применения.Исследования показывают, что при пляске наряду с выраженными вертикальными движениями проводов имеют место синхронизированные с ними крутильные колебания.Закручивание провода приводит к дополнительному увеличению подъемных аэродинамических сил и, как следствие, амплитуд колебаний по сравнению с «чистым» вертикальным движением проводов.Поэтому управление крутильными колебаниями является одним из эффективных способов защиты проводов ЛЭП от низкочастотных колебаний.Для этого используются маятниковые гасители различных конструктивных схем

The paper utilizes a nonlinear viscoelastic model of a medium with associative and hereditary memory in the form of a system of integro-differential equations. The hereditary memory is contained (for a long time) in the Volterra integral operator, and the associative (short-term) memory is determined by the differential operator. Identification of the model is solved using neural networks in the version of the finite-dimensional approximation with discrete time for a composite material based on a matrix of natural rubber (polyisoprene), filled by 20% with N-330 carbon black. The study is carried out in both the small strain mode and the finite strain mode. The issues studied in the paper are the accuracy of reproduction by the model of the real nonlinearity function and its ability to generalize the experimental material on the basis of the training sample. The identification of this model showed a good reproduction of the actual function of nonlinearity of a real viscoelastic material in the finite strain mode.

This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.

A phenomenological approach which we refer to as kinematic is proposed to describe hysteresis; according to this approach, the force and kinematic parameters of a mechanical system are related by a first-order ordinary differential equation. The right-hand side is chosen in the class of functions ensuring the asymptotic approach of the solution to the curves of the enveloping (limit) hysteresis cycle of steady-state vibrations. The coefficients of the equation are identified by experimental data for the enveloping cycle. The proposed approach permits describing the hysteresis trajectory under the conditions of unsteady vibrations with an arbitrary starting point inside the region of the enveloping cycle. As an example, we consider the problem on forced vibrations of a pendulum-type damper of low-frequency vibrations.

An algorithm for numerical simulation of one-dimensional detonation using a one-stage irreversible model of chemical kinetics is proposed. The discretization of the convective parts of governing equations is made in accordance with the balance-characteristic CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The approximation of source terms is performed implicitly without splitting into physical processes with a regulated order of approximation. It is shown that the numerically obtained Chapman-Jouget detonation parameters are in exact agreement with the analytical solution. It is also shown that, in the case of unstable detonation, the numerical results are dependent on the order of approximation chosen for the right-hand sides of the governing equations.

A number of known phenomenological models are considered, which are used to describe a variety of hysteresis effects in nature.In this case, the system is considered as a "black box" with known experimental values of input and output parameters.Correlations between them are established by mathematical functions, whose parameters are identified using experimental data.Amongthe phenomenological models there are marked the Bouc-Wen model andits analogsthat have been successfully usedin variousscientific and technical fieldsdue to the possibilityof the analytical description ofvarious hysteresis loopsof non-stationary processes.The conditions are formulatedwhich must be satisfied by the Bouc-Wen model.The main ones are the model adequacy of the physical process and stability.To describe the hysteresis, a mathematical model is suggested, according to which the force and kinematic parameters are bound by a special differential equation of the first order.In contrast to the Bouc-Wen model, the right side of this equation is chosen in the form of a polynomial of two variables determining the trajectory of a hysteresis in the process diagram.It is stated that this presentation provides the asymptotic approximation of the solution to the curves of the comprehending (including) hysteresis cycle.This cycle is formed by curves of direct and reverse processes ("loading-unloading" processes), which are based on experimental data for the maximum possible or permissible intervals of parameter changes during the steady vibrations.Coefficients in the right part are determined from experimental data for the comprehending hysteresis cycle under conditions of steady-state oscillations.Approximation curves of the comprehending cycle are constructed using the methods of minimizing the discrepancy of analytical representations to the number of experimental points.The proposed approach allows by one differential equation to describe the trajectory of hysteresis with a random starting point within the area of the comprehending cycle.

At present the theory and calculation of single-stage high-pulse transformer (PT) are well developed. Their characteristics are determined depending on the type and load parameters. However, the method of calculation of PT executed in cascade is not fully developed. The main advantage of the cascade scheme is the transfer of the insulation from the inside to the outside. Due to this electric field intensity can be reduced at the inner insulation number of times, the number of PT components in cascade. The paper presents the results of comparative experimental studies of the characteristics of single-stage and two-stage PT included in the resistive load and recharge mode capacitive storage through to PT exacerbates capacity. There are considered two types of PT with the same ratios, the number of turns of the windings and the section of magnetic cores, but different magnetic properties of the cores. The methodology of comparative research is to determine the forming properties of one- and two-stage PT schemes in the storage capacitor discharge on resistive and capacitive load across PT with following oscilloscope current and voltage at the load. Comparative studies have defined the scope of the cascade of PT schemes. The paper shows that the multi-stage schemes of PT are highly ineffective in the pulse shaping circuits on resistive load as the inductive elements of the equivalent circuits cascade PT form an inductive voltage divider. It has been shown that the cascade circuit is effective in PT overcharge mode sharpened on capacitive storage capacity in the matching mode, while the efficiency of such schemes is close to 100 %, and those positive properties possessed by the cascade circuits are realized.