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Vibrations in engineering and technology

space SCIENTIFIC JOURNALS OF VINNITSA NATIONAL AGRARIAN UNIVERSITY

Issue №: 3 (94)

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


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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USING OPERATOR METHOD AND EFROS TRANSFORM FOR TAKING INTO ACCOUNT DISSIPATIVE PROPERTIES OF DEFORMABLE STRUCTURAL ELEMENTS

DOI: 10.37128/2306-8744-2019-3-11
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Voropay Alexey Valerievich – Candidate of Technical Sciences, Assosiate Professor, National Technical University "Kharkov Polytechnic Institute", Kharkov; tel.: (050) 524-92-54; e mail: voropay.alexey@gmail.com.

Annotation

An approach for taking into account the dissipative properties of deformable structural elements (and in particular internal friction in the material) is proposed. This approach, based on the operator method and Efros transformation, is applied to analytical solutions obtained in the framework of elasticity theory, which can be represented as integrals of convolution type. The direct Laplace transform is applied to the operator equation. It is shown in the paper that changing to the Laplace variable enables one to pass from the relations taking into account dissipation energy to those for an elastic plate in the image space. The Efros theorem is used to perform the inverse Laplace transform of the complex function obtained. The posed problem is reduced to finding an unknown transforming function. Numerical calculations showed that in the problem considered (for small values of the time variable) the law of this function variation is very close to the law of normal distribution (Gaussian) with variable dispersion.
Since the integral equations are discretized the kernel numerical modification is proposed by the Efros theorem. This modification is carried out by multiplying the discrete analogs of the original kernels by the special matrix obtained on the basis of the Gauss integral.
The example of computing elastic and viscoelastic plate deflection is given, kernels of convolution integrals are presented for the "elastic" solution taking into account dissipation energy (internal friction in the material of the plate). Transversal impulse action on rectangular isotropic plates of medium thickness is considered. The plates are assumed to be hinged along the whole boundary. The plate deforming is simulated by the Timoshenko’s refined theory. It is possible to relatively quickly recalculate the deflections and deformations of the plate, taking into account internal friction for different values of the dissipation coefficients.

Keywords: medium-thickness viscoelastic plate, nonstationary deforming, dissipative properties, internal friction, Laplace transformation, Efros theorem.

List of references

1. Filippov A. P. Kolebaniya deformiruyemykh sistem [Oscillations of deformable systems]. Moscow, Mashinostroyeniye Publ., 1970. 734 p. [In Russian].
2. Yanyutin Ye. G., Yanchevskiy I. V., Voropay A. V., Sharapata A. S. Zadachi impul'snogo deformirovaniya elementov konstruktsiy : Monografiya [Problems of pulse deformation of structural elements : Monograph]. Kharkov, KHNADU Publ., 2004. 392 p. [In Russian].
3. Grigor'yev A. L., Moldavskiy E. A., Tartakovskiy I. I. Operatornyy metod rascheta vynuzhdennykh kolebaniy vyazkouprugoy mekhanicheskoy sistemy [Operator method for computing induced oscillations of viscoelastic mechanical system]. Tezisy dokladov IV Vsesoyuznoy konferentsii. "Sovremennyye problemy stroitel'noy mekhaniki i prochnosti letatel'nykh apparatov". Khar'kovskiy aviatsionnyy institut im. N. Ye. Zhukovskogo [Theses of the IV All-Union Conferrence “Contemporary problems of constructural mechanics and aircraft durability”  N. E. Zhukovskiy Kharkov Aviation Institute]. Khar'kov, Tipografiya KHVVKIURV Publ., 1991. 78 p. [In Russian].
4. Grunauer A. A., Tartakovskiy  I. I., Grigor'yev  A. L. O svyazi sily pruzhiny s zakonom yeye deformirovaniya [On the relation between spring strength and its deformation law]. Teoriya mekhanizmov i mashin : Resp. mezhduved. nauch.-tekhn. sb. [Theory of  mechanisms and machines : Republican Interdepartamental Scientific and tTechnical Digest]. Kharkiv, Vishcha shkola. Izd-vo pri Khar'k. un-te Publ., 1985, no. 39, pp. 7–22. [In Russian].
5. Ditkin A. V., Prudnikov A. P. Integral'nye preobrazovaniya i operatsionnoe ischislenie [Integral transforms and operational calculus]. Moscow, Gosudarstvennoye izdatel'stvo fiziko-matematicheskoy literatury Publ., 1961. 524 p. [In Russian].
6. Krasnov M. L., Kiselev A. I., Makarenko G. I. Funktsii kompleksnogo peremennogo. Operatsionnoe ischislenie. Teoriya ustoychivosti : Uchebnoe posobie, 2-e  izd., pererab. i dop. [Functions of complex variable. Operational calculus. Stability theory: Textbook, 2-nd edt., revised and expanded]. Moscow, Nauka. Glavnaya redaktsiya fiziko-matematicheskoy literatury Publ., 1981. 305 p. [In Russian].
7. Yanyutin Ye. G., Voropay A. V. Identifikatsiya impul'snogo nagruzheniya uprugoy pryamougol'noy plastiny [Identification of pulse loading of elastic rectangular plate]. Prykladna mekhanika [Applied mechanics]. 2003, vol. 39, no. 10, pp. 97–102. [In Russian].

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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.