Simulation of oscillatory processes in the MVSTUDIUM package

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

Investigation of the influence of an additional viscoelastic support mass-inertial characteristics on the rectangular plate non-stationary deformation

Modeling additional supports that affect the non-stationary deformation of lamellar structural elements is associated with a number of idealizations and assumptions. Many sources describe the deformation of supported structural elements using absolutely rigid additional supports or stiffeners. In reality, additional supports have viscoelastic properties (viscous and elastic components). When studying non-stationary vibrations, one should also take into account the mass-inertial properties of additional supports. Goal. The goal of the work is: 1) refinement of the existing mathematical model of an additional viscoelastic support by taking into account the influence of its mass-inertial characteristics; 2) study of the influence of these characteristics on the non-stationary deformation of a rectangular plate. Methodology. The non-stationary deformation of beams or plates is described by systems of partial differential equations. For these objects, good results are given by models based on the hypotheses of S.P. Timoshenko, taking into account the inertia of rotation and shear. Such systems of equations can be solved by expanding the sought functions (displacements and angles of rotation) in the corresponding series and using the direct and inverse integral Laplace transform. The determination of the unknown reaction of the additional viscoelastic support, taking into account its mass-inertial characteristics, is carried out on the basis of solving the Volterra integral equations. Results. In this work, an analytical and numerical solution in a general form is obtained, which makes it possible to determine the dependence of the change in time of reaction between the plate and the additional support for various parameters of the mechanical system. Originality. The solution to this problem is based on the further development by the authors of an approach to modeling additional supports in the form of additional unknown non-stationary loads, which are determined from the analysis of Volterra integral equations. Practical value. Examples of calculations for the considered mechanical system at three different values of mass are given. It is shown that the mass-inertial characteristics of the additional support cause a noticeable effect on the oscillatory process, and the changes concern both amplitude and phase characteristics.

Determination of natural frequencies of railway track elements under train load and selection of resilient shock absorbers

Objective: To outline the theoretical and methodological foundations of the railway track oscillation frequency analysis. To justify the need to assess the level of vibrodynamic impact of rolling stock on the elements of the track superstructure and the roadbed. To provide a methodology for calculating the oscillation parameters. To evaluate the effectiveness of the use of shock-absorbing elements. Methods: The modeling of the oscillatory process of the railway track elements and the analysis of physical models of oscillations were used. Results: The applicability of assessing the level of vibrodynamic impact of rolling stock on the elements of the track superstructure and the roadbed has been confirmed. A physical model of the vibrodynamic force impact of railway rolling stock and the responses of track infrastructure elements is described. The procedure for calculating the natural frequencies of the elements of the track superstructure and the roadbed and the characteristics of the shock-absorbing elements is given. Practical importance: The presented methods for calculating the natural frequencies of the elements of the track superstructure and the roadbed, as well as the characteristics of resilient shock-absorbing elements – rail shock pads and sleeper pads – make it possible to evaluate the effectiveness of their use to reduce the level of vibrodynamic impacts, to protect against resonance, and ensure the train traffic safety.

Optimal control of pulse compensators of oscillatory phenomena in a network oil and gas pipeline system

Within the framework of oil and gas engineering, the problem of optimal control of pulse compensators that counteract harmful oscillatory phenomena in a continuous medium during transportation via network gas-hydraulic carriers is considered. Powerful compressor units that create high pressure in the carrier of a continuous medium, to a large extent contribute to the formation of undesirable oscillatory phenomena (pulsations) that occur at the output of these compressors. These ripples are transmitted to the network carrier environment, which significantly reduces the efficiency of compressor units and even causes accidents in the networks of gas and hydraulic carriers. The latter means that the software engineering of the oil and gas industry should include research in the direction of improving the reliability of operation of compressor units and gas-hydraulic carriers. In the presented study, the mathematical description of the oscillatory process of a continuous medium is carried out by formalisms of a differential-difference system of hyperbolic equations with distributed parameters on a graph. At the same time, the mathematical model contains a fairly accurate mathematical description of controlled pulse compensators. The problem of controlling pulse compensators of an oscillatory process is considered as the problem of a point control action on a controlled differential-difference system at the places where continuous medium vibration dampers are connected to a network carrier. This is a characteristic feature of the presented study, which is quite often used in practice when engineering the processes of transporting various kinds of continuous media through network oil and gas carriers. The study essentially uses the conjugate state and the conjugate system for a differential-difference system - the relations determining the optimal point control are obtained. The results of the work are applicable in the framework of oil and gas engineering to the study of issues of stabilization and parametric optimization.

Application of modal and harmonic analysis to predict the automotive transmission vibration at an early stage of design

Introduction (problem statement and relevance). The need to increase the operating speeds and input torque of automobile transmissions because of their vibration is becoming a more and more urgent problem.The purpose of the study was to substantiate the applicability of harmonic analysis, which makes it possible to determine the actual values of vibration values during a steady oscillatory process, for the initial assessment of the gearbox vibration activity.Methodology and research methods. The calculation of the gearbox vibration activity was carried out by modal and harmonic analyses, implemented by the finite element method, and followed by the experimental study of gearbox vibration on a test bench.Scientific novelty and results. The presented experimental and calculated results of the research show that the difference between the experimental and calculated values is no more than 4.2%. This proves the possibility of applying modal and harmonic analysis to predict the gearbox vibration state at an early stage of product design at the stand.Practical significance. The given calculation algorithm makes it possible to predict, with a sufficient degree of accuracy, the vibration of the gearbox before the manufacture of a prototype in experimental production.

Novel generic models for differentiating stem cells reveal oscillatory mechanisms

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington’s epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario, gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario, two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process.

Mechanical and mathematical modeling of seismic shear vibrations of a glacial massif

В статье впервые в мире разработаны теоретические положения сдвиговых сейсмических колебаний ледникового массива. Актуальность представленных научных разработок в приложении к инженерной сейсмологии и гляциологии обусловлено тем, что в недавнее время в различных регионах нашей планеты имели место внезапные срывы с гор грандиозных масс льда, что приводило к образованию мощных гляциальных селевых потоков. Эти потоки уничтожали населенные пункты и народохозяйственные объекты с многочисленными жертвами. Все мы помним катастрофический сход ледника Колка в Геналдонском ущелье в 2002г., унесшего 125 человеческих жизней. Причиной срыва ледяных масс со своих подстилающих поверхностей примерзаний является динамическое воздействие, в качестве которого мы рассматриваем землетрясение. Цель исследования. На основе современных научных методов механики сплошных сред проведение механико-математического компьютерного моделирования колебательного процесса в ледниковом массиве, когда колебание спровоцировано гармонической сейсмической волной, упавшей на подстилающую поверхность примерзания массива. В рамках выполненного моделирования содержится постановка и решение соответствующей начально-краевой задачи. Начальными данными являются как физико-механические характеристики льда, его плотность, модуль сдвига, коэффициент внутреннего (вязкого) сопротивления, так и геометрические размеры и непризматическая конфигурация массива. Искомыми величинами в поставленной начально-краевой задаче являются перемещения и напряжения, как в самом теле массива, так и на подстилающей поверхности примерзания. Методы исследования. Составленная модель представляет собой начально-краевую задачу математической физики для дифференциального уравнения гиперболического типа, в котором один коэффициент является комплексной величиной, названной комплексным модулем сдвига согласно с гипотезой Е.С. Сорокина, а другой коэффициент является переменной величиной, зависящей от пространственной координаты. Эти два особых фактора создают трудности в аналитическом способе решения начально-краевых задач. В представленной работе найден путь решения поставленной задачи в частном случае – при экспоненциальной зависимости переменного коэффициента от пространственной координаты. Результаты работы. Получена совокупность расчётных формул для вычисления напряжений и деформаций в ледниковом массиве. Доказано утверждение о том, что низкобалльная сейсмическая околорезонансная волна может отколоть ледниковый массив от подстилающей поверхности примерзания, что приведет к образованию гляциального селевого потока Theoretical studies of seismic oscillations of the glacial massif are an urgent task in the field of engineering seismology and glaciology. This statement is confirmed if we recall the case of the sudden catastrophic collapse of the Kolka glacier in 2002, which claimed the lives of 125 human lives. Aim. Conducting a mechanical and mathematical simulation of the oscillatory process in a glacial massif, when the oscillation is triggered by a harmonic seismic wave that has fallen on the underlying surface of the frozen massif. Formulation and solution of the initial boundary value problem for calculating stresses and deformations in a glacial massif. Methods. The compiled model represents an initial boundary value problem of mathematical physics for a hyperbolic differential equation, in which one coefficient is a complex quantity called the complex shift modulus according to the hypothesis of E.S. Sorokin, and the other coefficient is a variable value depending on the spatial coordinate. These two special factors create difficulties in the analytical way of solving initial-boundary value problems. In the present paper, we find a way to solve the problem in the special case - with an exponential dependence of the variable coefficient on the spatial coordinate. Results. A set of calculation formulas for calculating stresses and deformations in the glacial massif is obtained. It is proved that a low-point seismic near-resonant wave can break off the glacial massif from the underlying freezing surface, which will lead to the formation of a glacial mudflow.

Influence of Impulse Moments On Single-Frequency Torsional Oscillations of Nonlinearly Elastic Bodies

Analytical study of the impulse moment influences on the nonlinear torsional oscillations in the homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types has been developed. For the case when the elastic material properties meet the body close to the power law of elasticity, mathematical models of the process are obtained. They are the boundary value problems for an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of pulse momentum on the oscillatory process. The peculiarities of resonant oscillations are established. Relative torsional oscillations of a nonlinear elastic body that rotates around the axis with a constant portable angular velocity are considered, taking into account the periodic action of pulse momentum acting in a fixed cross-section. The reliability of the obtained calculation formulas is confirmed.

Use of the pass-through method to solve sound radiation problems of a spherical electro-elastic source of zero order

In the article was solved the problem of radiation of a sound by the electroacoustic transducer which is executed in the form of a thin spherical cover, using a pass-through method. The outer and inner surfaces of the shell are completely electroded. The application of this method provides an opportunity to avoid inaccuracies that arise during the traditional formulation of boundary conditions for acoustic mechanical fields, the use of equivalent substitution schemes and the absence of boundary conditions for the electric field in general. Given methodology eliminates these shortcomings by applying conjugation conditions, taking into account the types of electroding of the surfaces of piezoceramic transducers, the introduction of boundary conditions for current and voltage. The results of the solution demonstrate the high capabilities of this pass-through method, in terms of taking into account the peculiarities of determining the characteristics of these fields, values and dependences of the main complex characteristics of the electroelastic transducer, and auxiliary material constants of the piezoelectric material. The proposed approach is relevant, because it allows to increase the reliability of modeling the operating conditions of acoustic transducers in the context of wave problems of acoustics. Aim is to enhance the range of performances and build algorithms solving problems of stationary mode hydroelectroelasticity sound radiation. The expected results are presented in terms of improving approaches to studying the features of the oscillatory process of the active elements of sound-emitting systems and the accompanying effects of the transformation of interconnected fields involved in the formation of the acoustic signal in the liquid