Issue №: 3 (94)
The journal deals with the problems of vibration technologies and machines, mathematical methods of vibration process studies, information on design and technological development, presents teaching and methodological aspects of teaching in the Higher School of Applied Sciences, where vibration machines and technologies are studied.
ESTABLISHMENT OF CONDITIONS FOR EFFECTIVE ARRANGEMENT OF A CIRCLE WITH RESPECT TO A SQUARE AND AN EQUILATERAL TRIANGLE WITH A COMMON CENTER FOR ESTIMATING THE LENGTH OF THE LINE OF DISAGREEMENT
DUBCHAK Viktor – Candidate of Technical Sciences, Associate Professor of the Department of Mathematics, Physics and Computer Technologies, Vinnitsa National Agrarian University (21008, 3, Sonyachna Str., Vinnytsia, e-mail: viktor_dubchak@rambler.ru).
In this paper we investigate the question of the optimal, extreme (minimum) location of one plane figure, namely, the square in the first case, as well as the equilateral triangle in the second case relative to the circle with the common center of the said figures. In comparison with previous works, the analysis of studies of such a mutual effective location continues. But if in the previous results a function based on determining the value of an area over which the geometric figures did not match was calculated and investigated, then in these studies another numerical characteristic, such as a function, is proposed as such a criterion for the basic working function. which determines the length of the total polygon (straight or arc, etc.). For certain ratios of the radius of a circle with respect to the length of the side of a square or triangle, the length of the arc of the total line along which the discrepancy between the specified geometric objects is observed will take on an extreme (minimum) value. The optimality of such mutual arrangement of one figure relative to another is evaluated by such a criterion as the effective estimation of the length of the set of lines by which the divergence of these figures occurs. The value of a certain function, which determines the length of such sum of lines of divergence of figures in both cases, is obtained, the study of the extremality of this function is performed, it is shown that at the found extremum point, the function that determines the total length of the line of divergence of figures acquires a minimum value. A study of a function that establishes the entire length of the line over which the discrepancy of the figures is observed indicates, at the extreme, that the function acquires minimal values in the case of such arrangement of figures, when the circle is inscribed squarely or an equilateral triangle, and when described around these figures when such a function is maximized. Drawings are given for a better understanding of the formulation and solution of the task, conclusions are drawn, which summarize the values of the arguments sought when the corresponding function acquires minimum values.
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About the journal
The journal "Vibrations in Engineering and Technologies" is included in the list of technical scientific publications of Ukraine
(Category "B", Order of the Ministry of Education and Science of Ukraine dated July 2, 2020 No. 886)
Old version of the site: http://vibrojournal.vsau.edu.ua/
The journal "Vibrations in Engineering and Technology" is indexed by the following databases and catalogs:
The certificateof massmedia State registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University
The journal is devoted to highlighting current issues in engineering, mechanical engineering, and technological processes, including the study of dynamic and oscillatory phenomena in technical systems, the application of mathematical methods for process modeling and analysis, as well as the presentation of results of design-engineering and technological developments. Particular attention is given to the study of vibration processes and their application in modern technologies.
The purpose of the scientific journal “Vibrations in Engineering and Technologies” is to disseminate the results of fundamental and applied research in the field of engineering sciences aimed at developing theoretical foundations and practical approaches to the design, analysis, and improvement of machines, materials, and technological processes, including the use of vibration and oscillatory effects in various sectors of production.
The publication is focused on the formation of a modern scientific and informational environment for the effective exchange of research results, support of innovative development, and implementation of advanced technical solutions in industry, agro-industrial production, and related fields.
The journal promotes the development of interdisciplinary research, the integration of modern engineering approaches, and the enhancement of the efficiency of technological processes and technical systems, including through the rational use of vibration phenomena.
Objectives of the Scientific Journal
To achieve its stated purpose, the journal addresses the following key objectives:
dissemination of results of fundamental and applied scientific research in the fields of mechanics, mechanical engineering, technological processes, machine dynamics, and equipment, as well as in areas related to the application of vibration phenomena in engineering and technologies;
promotion of research aimed at the creation and improvement of machines, mechanisms, and technological equipment based on oscillatory and vibration processes;
support for the implementation of modern technological solutions focused on improving productivity, energy efficiency, and reliability of technical systems;
обеспечение scientific exchange of research results among research institutions, higher education establishments, and industrial enterprises;
development of interdisciplinary cooperation among researchers in the fields of mechanics, materials science, material processing technologies, and automation of technological processes;
dissemination of modern scientific achievements and advanced technologies related to the application of vibration processes in production and technical systems.
Publisher Vinnytsia National Agrarian University
In June 1994 the 2nd International Scientific and Technical Conference "Application of vibrations for technological purposes" was organized on the basis of Vinnytsia State Agricultural Institute. Leading experts in this field, noting the significant contribution to the school of Vibration Engineering under the leadership of P. S. Bernyk, proposed to create a professional all-Ukrainian scientific and technical journal "Vibration in engineering and technology..The journal was foundedat Vinnytsia State Agricultural Institute and P.S. Bernyk was elected to be the chief editor .
For all these years (since 1994) theJournal "vibration in engineering and technology" published 119 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Ihor Kupchuk, Candidate of Technical Sciences, Associate professor, Associate Professor of the Department of Engineering Mechanics and Technological Processes in the Agricultural Industry Faculty of Engineering and Technology Vinnytsia National Agrarian University is the chief editor of the "Vibrations in engineering and Technology"
The journal "Vibration in Engineering and technology", which has no analogues on the territory of Ukraine, is well known abroad.
