Modeling vibrations of a beam with one fixed and another free end using fractional integrodifferentiation

2020 ◽  
Vol 20 (3) ◽  
pp. 19-23
Author(s):  
S.Sh. Rekhviashvili ◽  
◽  
A.V. Pskhu ◽  
A.M. Kidakoev ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Analytical Form ◽  
Dynamic Hysteresis ◽  
Fractional Integrodifferentiation

A mathematical model of vibrations of a beam with one fixed and another free end has been developed, taking into account the effect of dynamic hysteresis, which is described using fractional integro-differentiation. The solution of the model equation is found in analytical form. The use of the fractional integro-differentiation makes it possible to correctly describe the dissipative nature of the beam vibrations.

scholarly journals A Mathematical Model for Predicting the Winnowing Efficiency of Bambara Groundnut Sheller

2020 ◽  
Vol 5 (2) ◽  
pp. 225-228
Author(s):  
Inimfon Samuel Ossom ◽  
Akindele Folarin Alonge ◽  
Kingsley Charles Umani ◽  
Edidiong J. Bassey
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Moisture Content ◽  
Model Equation ◽  
Model Simulation ◽  
Least Square Method ◽  
Bambara Groundnut ◽  
Least Square ◽  
Predicted Model ◽  
Experimental Values

A mathematical model for predicting the winnowing efficiency of bambara groundnut sheller was developed. The regression equation for model simulation was developed using Least Square Method. The model was verified and validated by fitting it into established experimental data from winnowing efficiency of already existed Bambara groundnut sheller. The result revealed that the fitted model correlated well with the experimental data with R-square value of 0.99. The winnowing efficiency obtained from the predicted model was approximately the same values with the experimental values. Therefore, the model equation was considered to be reasonably good for predicting the winnowing efficiency of bambara groundnut sheller for known values of moisture content and blower speed.

scholarly journals Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

2019 ◽  
Vol 14 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Matvey Kulakov ◽  
E.Ya. Frisman
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Temporal Dynamics ◽  
Local Population ◽  
Two Dimensional ◽  
Attraction Basin ◽  
Local Populations ◽  
Long Range Interactions ◽  
Spatio Temporal ◽  
Formation Of Groups

The paper proposed a mathematical model for spatio-temporal dynamics of two-age populations coupled by migration living on a two-dimensional areal. The model equation is a system of nonlocal coupled two-dimensional maps. We considered cases when populations are coupled in a certain neighborhood of different form: circle, square or rhombus. Special attention is paid to the situation when the intensity of the migrants flow between the territories decreases with increasing distance between them. For this model we study the conditions for the formation of groups of synchronous populations or clusters that form, in space, typical structures like spots or stripes mixed with solitary states. It is shown that the dynamics, in time, of different clusters may differ significantly and may not be coherent and correspond to several simultaneous multistable regimes or potential states of the local population. Such spatio-temporal regimes are forced and are caused by impacts or perturbations on a single or several populations when their number falls into the attraction basin of another regime. With strong coupling, such clusters are rare and are represented by single outbursts or solitary states. However, the decrease in the coupling strength leads to the fact that these outbursts cause oscillations of their neighbors, and in their neighborhood a cluster of solitary states is formed which is surrounded by subpopulations with a different type of dynamics. It was found that the interaction of different type of clusters leads to the formation of a large number of groups with transitional dynamics that were not described for local populations.

scholarly journals THE METHOD OF FINDING ADEQUATE MATHEMATICAL MODELS DESCRIBING THE CHARACTERISTICS OF RADIO ENGINEERING DEVICES

2021 ◽  
Vol 2 (336) ◽  
pp. 145-151
Author(s):  
P. V. Boikachov ◽  
A. A. Yerzhan ◽  
V. O. Isaev ◽  
I. A. Dubovik ◽  
A. Marat
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Experimental Studies ◽  
Statistical Processing ◽  
Analytical Form ◽  
Physical Processes ◽  
Technical Object ◽  
Radio Engineering ◽  
Input Action ◽  
The One

The method of finding adequate mathematical models of radio engineering devices in an analytical form is proposed. RES, as a rule, is a very complex technical object that includes a large number of components with diverse connections between them, the hierarchy of construction of which can be represented in the form of a kind of pyramid. In this regard, there is a simulation of radio-electronic devices, which can be carried out at all levels of the "pyramid". Modeling at its lower levels, including semiconductor devices, links, cascades, etc., is reduced to describing their operation using a matrix, equation, formula, graph, or table. Such a mathematical model should, on the one hand, accurately reflect the physical processes in the object under study, and on the other - be suitable for use on a PC. In some cases, the mathematical model is the result of analytical or numerical analysis of the physical model of the object, but most often-experimental studies. Processing, including statistical processing, of the available data array that characterizes the operation of the cascade or element, is carried out using a PC. The operation of an object can also be defined in the form of its response or reaction to an input action without penetrating into the essence of the physical processes occurring inside the device.

scholarly journals Modeling of electrodynamic processes in self-organization of fractal-convective cloud structures

2020 ◽  
pp. 63-70
Author(s):  
Т.С. Кумыков
Keyword(s):  
Dynamic Process ◽  
Model Equation ◽  
Crystallization Front ◽  
Convective Cloud ◽  
Analytical Form ◽  
The Self ◽  
Potential Difference ◽  
Numerical Calculations ◽  
Self Organization ◽  
Cloud Environment

В работе рассмотрена модель электроо-динамического процесса возникновения больших потенциалов на фронте кристаллизации при самоорганизации конвективных облачных структур, в котором учитывается фрактальность облачной среды. В аналитическом виде найдено решение уравнения модели. С помощью численных расчетов показано зависимость разности потенциала от фрактальности среды и зависимость уровня фрактальной зоны от радиуса частицы. The paper considers a model of fractal-dynamic process of occurrence of large potentials on the crystallization front in the self-organization of convective cloud structures, which takes into account the fractality of the cloud environment. The solution of the model equation is found in the analytical form. With the help of numerical calculations demonstrate the dependence of the potential difference from the fractality of environment and the dependence of the level of the fractal of the radius of the particle.

Применение беспилотных летательных аппаратов в обеспечении технологической безопасности// Journal of Technical and Natural Sciences 5(14), 2019/ RELF Group & OEAPS Inc.(Open European Academy of Public Sciences); Chief Editor Vitaly Yakovlev- Berlin, Germany. 26.09.2019: OEAPS Inc., 2019. - PP. 54-90.

2019 ◽  
Author(s):  
Л.П. Варламова
Keyword(s):  
Mathematical Model ◽  
Control Object ◽  
Analytical Form ◽  
Chief Editor ◽  
Sensor Data ◽  
European Academy ◽  
Sufficient Detail ◽  
Aerial Vehicle ◽  
Flight Route ◽  
Adaptation Task

В работе рассматриваются две части: первая часть - разработка и моделирование системы управления мультироторным беспилотным летательным аппаратом, вторая часть – применение беспилотных летательных аппаратов в обеспечении технологической безопасности. Предложено использование математической модели мультироторного беспилотного летательного аппарата при построении системы управления. Беспилотный летательный аппарат рассматривается как объект управления, для которого необходимо решить задачу адаптации при построении маршрута. По причине маневренности и небольших габаритных размеров беспилотные летательные аппараты могут быть использованы для контроля крупногабаритных технологических аппаратов, трубопроводов в аварийных ситуациях или близких к ним.The use of the hexacopter mathematical model in the construction of a control system is proposed in this paper. An unmanned aerial vehicle is considered as a control object, for which it is necessary to solve the adaptation task when constructing a route.The aim of the research in this paper is to optimize the control of the UAV when constructing a flight route based on a mathematical model of a multi-rotor aircraft. This is due to the peculiarities of the movement of the multi-rotor UAV under various meteorological conditions.Multicopter (hexacopter) is described in sufficient detail in the literature. The position and orientation of the hexacopter in the earth’s coordinate system are determined by the three coordinates x, y, z and the three Euler angles. The positive directions of all turns correspond to counterclockwise rotation, along the axis of rotation to the origin.Based on the satellite navigation sensor data at the first stage, the initial and of course the state of the object are initiated, which will correspond to the required maneuver. The UAV route in the analytical form of the solution to the problem of finding the optimal speed control is based on the Pontryagin maximum principle. An alternative could be the extensive reversal method based on the Euler theorem on the final rotation of a rigid body having a fixed point.

Влияние фрактальной структуры на электрическое поле в грозовых облаках

2021 ◽  
pp. 84-91
Author(s):  
T.S. Kumykov
Keyword(s):  
Mathematical Model ◽  
Fractal Dimension ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Fractal Structure ◽  
Close Connection ◽  
Static Electric Field ◽  
Fractal Medium ◽  
Fractional Integrodifferentiation

The paper considers the degree of fractal structure impact on the electric field intensity inside thunderstorm clouds using the apparatus of fractional integrodifferentiation. We propose a mathematical model of intensity dynamics of a static electric field in the thunderstorm clouds, taking into account media with fractal dimension. The results obtained confirm the close connection of electrophysical processes in thunderclouds with the fractal medium itself. В статье с помощью аппарата дробного интегро-дифференцирования рассматривается степень влияния фрактальной структуры на напряженность электрического поля внутри грозовых облаков. Предлагается математическая модель динамики напряженности статического электрического поля в грозовых облаках с учетом сред с фрактальной размерностью. Полученные результаты подтверждают тесную связь электрофизических процессов в грозовых облаках с самой фрактальной средой В статье с помощью аппарата дробного интегро-дифференцирования рассматривается степень влияния фрактальной структуры на напряженность электрического поля внутри грозовых облаков. Предлагается математическая модель динамики напряженности статического электрического поля в грозовых облаках с учетом сред с фрактальной размерностью. Полученные результаты подтверждают тесную связь электрофизических процессов в грозовых облаках с самой фрактальной средой.

scholarly journals A Method for Preliminary Estimation of the Length of Midship Body Block to Be Inserted During Ship’s Conversion

2017 ◽  
Vol 24 (1) ◽  
pp. 42-46 ◽  
Author(s):  
Jan P. Michalski
Keyword(s):  
Mathematical Model ◽  
Analytical Form ◽  
Investment Analysis ◽  
Preliminary Estimation

Abstract The paper presents a method for preliminary estimation of the length of the midship body block, which inserted in the original hull, increases the deadweight of the ship in line with a required quantity. The method may be useful for establishing the scope of conversion to better adjust the ship for transportation tasks. The problem is formulated by using a mathematical model so selected that its solution, under set of assumptions, is obtained in a closed analytical form. The presented method can be useful for application to pre-investment analysis of the ship conversion costs and functional profits.

scholarly journals Method for Tuning the Parameters of Active Force Reducing Building Vibrations—Numerical Tests

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8293
Author(s):  
Andrzej Dymarek ◽  
Tomasz Dzitkowski ◽  
Krzysztof Herbuś ◽  
Piotr Ociepka ◽  
Andrzej Niedworok ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Vibration Amplitude ◽  
Dynamic Properties ◽  
Maximum Amplitude ◽  
Analytical Form ◽  
Input Function ◽  
Active Force ◽  
Natural Vibrations ◽  
Richter Scale

The paper formulates a method of active reduction of structure vibrations in the selected resonance zones of the tested object. The method ensures reduction of vibrations of the selected resonance zones by determining the parameters of the active force that meets the desired dynamic properties. The paper presents a method for determining the parameters of the active force by reducing the vibrations of the structure in its resonance zones to a given vibration amplitude. For this purpose, an analytical form was formulated, which will clearly define the dynamic properties of the tested object and the force reducing the vibrations in the form of a mathematical model. The formulated mathematical model is a modified object input function, which in its form takes into account the properties of the active force reducing the vibrations. In such a case, it is possible to use the methods of mechanical synthesis to decompose the modified characteristic function into the parameters of the system and the parameters of the force being sought. In the formulated method, the desired dynamic properties of the system and the vibration reducing force were defined in such a way that the determined parameters of the active force (velocity-dependent function) had an impact on all forms of natural vibrations of the tested system. Based on the formalized method, the force reducing the vibrations of the four-story frame to the desired displacement amplitude was determined. Two cases of determining the active force reducing the vibrations to the desired vibration amplitude of the system by modifying the dynamic characteristics describing the object together with the active force were considered. For both cases, the system’s responses to the oscillation generated by harmonic force of frequencies equal to the first two forms of natural vibrations of the tested system were determined. In order to verify the determined force reducing the vibrations of the object and to create a visualization of the analyzed phenomenon, the building structure dynamics were analyzed with the use of PLM Siemens NX 12 software. The determined force parameters were implemented into the numerical model, in which the tested system was modelled, and the response time waveforms were generated with regard to the considered story. The generated waveforms were compared with the waveforms obtained in the formalized mathematical model for determining the active force reducing the vibrations. The vibrations of the tested numerical model were induced by the kinematic excitation with the maximum amplitude equal to 100 mm, which corresponds to the vibration amplitude during the earthquake with a force equal to level 5 on the Richter scale.

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