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Vibrations in engineering and technology

space SCIENTIFIC JOURNALS OF VINNITSA NATIONAL AGRARIAN UNIVERSITY

Issue №: 2(97)

Published: 1970.01.01
DOI: 10.37128/2306-8744-2020-2


Description:
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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DEFINITION OF KINEMATICS OF DEFORMATION BASED ON SPLINE-APPROXIMATIONS

DOI: 10.37128/2306-8744-2020-2-11
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Sivak Roman - Doctor of Technical Sciences, Associate Professor, Vinnytsia National Agrarian University (3 Sonyachna Street, Vinnytsia, Ukraine, 21008, e-mail: sivak_r_i@ukr.net).

 

 

 

Annotation

It is suggested to use smoothing cubic spline functions to approximate the current functions. The structure of the selected functional provides the minimum curvature of the spline and the smallest deviation of the spline from the function smoothed at the nodes. The necessary correlation between these requirements is provided by the choice of weights. The algorithm for approximating the current function is implemented by moving from a grid created by current lines and auxiliary lines to a rectangular grid. To reduce the effect of random errors of experimental information on the current line, a smoothing algorithm with a given accuracy was used. The current function is interpolated from the physical grid to the calculated one. The flow velocities were approximated to calculate the strain rates. To estimate the accuracy of the calculations, it is proposed to use the deviation from the incompatibility condition.

The main disadvantage is that their behavior around a point determines their behavior as a whole. In this regard, other approaches to the approximation free of this deficiency have been developed in recent years. One such approach that has proven itself well in both theoretical and practical applications is the use of so-called splines. Splines are called functions that are glued together from different pieces of polynomials by a fixed system. The simplest example is broken. Splines naturally occur in many mechanical problems. For example, the spline shape has an elastic beam with point loads. Among the splines, polynomial splines glued together from pieces of polynomials play the most important role. The development of the theory of such splines and their popularization were facilitated by I. Schoenberg's work. Polynomial splines are beginning to be used in many application problems related to function approximation.

 

Keywords: stress-strain state, quadrangular plate, orthotropic material, spline-collocation method, discrete orthogonalization method, coordinate transformation.

List of references

1. Del G. D. Tehnologicheskaia mehanika / G. D. Del. – М. : Mashinostroenie, 1978. – 174 s.

2. Ogorodnikov V. А. Otsenka deformiruemosti metallov pri obrabotke davleniem / V. А. Ogorodnikov. – К. : Vyscha shk., 1983. – 173 s.

3. Matvichuk V. А. Sovershenstvovanie protsessov lokalnoi rotatsionnoi obrabotki davleniem na osnove analiza deformiruemosti vetallov: monografia / V. А. Matvichuk, I. S. Aliev. – Kramatorsk : DGMA, 2009. – 268 s.

4. Mihalevich V. М. Tenzorni modeli nakopichennia poshkodzhen / V. М. Mihalevich. – Vinnitsia : UNIVERSUM-Vinnitsia, 1998. – 195 s.

5. Mihalevich V. М. Matematichne modeliuvannia mehaniki formoutvorennia pri holodnomu tortsevomu rozkochuvanni / V. М. Mihalevich, V. О. Kraevski. – Vinnitsia : UNIVERSUM-Vinnitsia, 2008. – 188 s.

6. Zavialov, Yu. S., Kvasov, B. Y., Myroshnychenko V. L. (1980). Metodu splain-funktsyi. M.: Nauka, [in Russian].

7. Suvorov, Y. K. (1973). Obrabotka metalov davlenyem. M.: Vussh. shk., [in Russian].

8. Ogorodnikov V. А., Derevenko I. A., Sivak R. I. (2018). On the Influence of Curvature of the Trajectories of  Deformation of a Volume of the Material by Pressing on Its Plasticity Under the Conditions of Complex Loading.  Materials Science, 54(3), 326–332. [in English].

9. Puzyr R., Kukhar V., Maslov A., Shchipkovskyi Y. (2018). The Development of the Method for the Calculation of the Shaping Force in the Production of Vehicle Wheel Rims. International Journal of Engineering & Technology, 7 (4.3) 30–34. [in English].

10. Maslov A., Batsaikhan J., Puzyr R., Salenko Y. (2018). The determination of the parameters of a vibration machinef the internal compaction of concrete mixtures. International Journal of Engineering & Technology, 7 (4.3). 12-19. [in English].

11. Puzyr R., Haikova T., Majerník J., Karkova M., Kmec J. (2018). Experimental Study of the Process of Radial Rotation Profiling of Wheel Rims Resulting in Formation and Technological Flattening of the Corrugations. Manufacturing Technology, 18 (1), 106–111. [in English].

12. Puzyr R., Savelov D., Shchetynin V., Levchenko R., Haikova T., Yasko S., Argat R., Sira Y., Shchipkovakyi Y. (2018). Development of a method to determine deformations in the manufacture of a vehicle wheel rim. Kravchenko, S.  Eastern-European Journal of Enterprise Technologies, 4 (1(94)), 55–60. [in English].

13. Puzyr R., Haikova T., Trotsko O., Argat R. (2016). Determining experimentally the stress-strained state in the radial rotary method of obtaining wheels rims. Eastern-European Journal of Enterprise Technologies, 4 (1(82)), 52–60. [in English].

14. Savelov D., Dragobetsky V., Puzyr R., Markevych A. (2015). Peculiarities of vibrational press dynamics with hard-elastic restraints in the working regime of metal powders molding. Metallurgical and Mining Industry, 2, 67–74. [in English].

15. Puzyr R., Savelov D., Argat R., Chernish A. (2015). Distribution analysis of stresses across the stretching edge of die body and bending radius of deforming roll during profiling and drawing of cylindrical workpiece. Metallurgical and Mining Industry, 1, 27–32. [in English].

 

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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

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

The certificateof massmediaState 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.