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

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.

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

NEWS OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN ◽

10.32014/2021.2518-1726.34 ◽

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.

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

Доклады Адыгской (Черкесской) Международной академии наук ◽

10.47928/1726-9946-2020-20-3-19-23 ◽

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.

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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.

10.31219/osf.io/3yvd6 ◽

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.

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

Energies ◽

10.3390/en14248293 ◽

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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On the influence of specimen thickness in TEM images of super-conducting vortices

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100166087 ◽

1996 ◽

Vol 54 ◽

pp. 724-725

Author(s):

J. Bonevich ◽

D. Capacci ◽

G. Pozzi ◽

K. Harada ◽

H. Kasai ◽

...

Keyword(s):

Flux Line ◽

Analytical Form ◽

Realistic Model ◽

Electron Holography ◽

Specimen Thickness ◽

Flux Tubes ◽

Analytical Expression ◽

Flux Lines ◽

Normal Core ◽

Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

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