Vibrations in engineering and technology


Issue №: 3 (94)

Published: 2019.06.26
DOI: 10.37128/2306-8744-2019-3

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.

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DOI: 10.37128/2306-8744-2019-3-7
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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.

Keywords: circle, square, equilateral triangle, length of arc of circle and its parts, length of part of side of square, extremality (minimum) of functions of one variable.

List of references

1. Dubchak V.M.(2018).  Vstanovlennya umov efektyvnoho pokryttya ploshcheyu kruha ploshchi kvadrata ta deyaki vypadky uzahalʹnennya [Establishment of terms of effective coverage by an area circle of area of square and some cases of generalization] Vibrations in Engineering and Technology. – Science magazine. Issue 4(91).15- 20 [In Ukraine].

2. Akhtershev S.P.(2005). Zadachy na maksymum y mynymum

[Maximum and minimum tasks] St.Petersburg.:BHC-Petersburg [In   Russia].

3. Belyaeva E.S.(1977). Ekstremal'nyye zadachi [Extreme Problems] –Enlightenment. [In Russia].

4. Gabasov R.F.(1997). Ekstremal'nyye zadachi v sovremennoy nauke i prilozheniyakh [Extreme Problemsin Modern Science and Applications] –Sorov Educational Journal. [In Russia].

5. Galeev E.M.(1989). Kratkiy kurs teorii ekstremal'nykh zadach [A short course in the theory of extremal problems] – Training allowance. Moscow. Moscow State University. [In Russia].

6.Vasilyev F.P.(2002). Chyselʹni metody rozv'yazannya ekstremalʹnykh zadach

[Numerical Methods for Solving Extreme Problems]  – Science. [In Russia].

7. Matvichuk V.A.(2018). Vykorystannya lokalʹnykh dzherel elektroenerhiyi dlya optymizatsiyi struktury EES [Use of local electricity sources to optimize the structure of the power plant] –Bulletin of the Khmelnytskyi National University, Series: Technical Sciences. Issue  4. 98-101[In Ukraine].        

8. Pryamukhina N.V.(2016). Teoretyko-metodolohichni zasady rozvytku rehionalʹnoho  ekonomichnoho prostoru v umovakh transformatsiynykh zrushenʹ [Theoretical and methodological foundations of the development of the regional economic space in the conditions of transformational shifts]– Author's abstract dis…. Doctor of  Economics Sciences. Severodonetsk. [InUkraine].


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About journal

Topics of the journal:

The journal "Vibrations   in engineering  and technology" presents materials on the following issues

• Theory of processes and machines
• Mechanical Engineering and materialprocessing
• Processing and food production

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/

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Key information:
ISSN (print): 2306-8744
DOI: 10.37128/2306-8744

The certificateof massmedia State registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University

Kind of publication: journal
Type of publication : Scientific
Publication status: Domestic
Year of founding:
Periodicity: 4 times a year
Extent: 18.75 nominal printed pages
ISSN: 2306-8744 (printed version), (online)
Language of edition  : (mixed languages) Ukrainian, English
The scope of the distribution and the category of readers: national, foreign, teaching staff, scientists, businessmen.
Periodical is included in the list of scientific professional editions of Ukraine approved by the Order of Ministry of Education and Sciences of Ukraine from 21.12.2015 No. 1328.
The journal "Vibrations in engineering and technology" is included in the "Catalogue of periodicals of Ukraine".
Journal subscription can be executed in each post office department.
 Subscription Index is  99720.


Old version of site: http://vibrojournal.vsau.edu.ua/

History of journal:

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  94 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Kaletnik H.M  PhD , professor, academician NAAS 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.