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Vibrations in engineering and technology

space SCIENTIFIC JOURNALS OF VINNITSA NATIONAL AGRARIAN UNIVERSITY

Issue №: 1(100)

Published: 2021.03.23
DOI: 10.37128/2306-8744-2021-1


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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VIBRATIONS OF AN INSTANTLY LOADED DISSIPATIVE OSCILLATOR

DOI: 10.37128/2306-8744-2021-1-3
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Olshanskiy Vasyl Pavlovych – Doctor of Physical and Mathematical Sciences, Full Professor, Professor at the Department of Physics and Theoretical Mechanics Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; OlshanskiyVP@gmail.com, тел.: (066) 0100955

Slipchenko Maksym Volodymyrovych – Candidate of Technical Sciences (Ph. D.), Associate Professor, Associate Professor at the Department of Physics and Theoretical Mechanics Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; Slipchenko_M@ukr.net, тел.: (066) 7120989

Spolnik Oleksandr Ivanovych – Doctor of Physical and Mathematical Sciences, Full Professor, Head of the Department of Physics and Theoretical Mechanics Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; alexspo@ukr.net, (067) 764-84-64

Solona Olena – Candidate of Technical Sciences (Ph. D in Engeneering), Associate Professor of the Department of General Technical Disciplines and Labor Protection, Vinnytsia National Agrarian University (3, Solnyschaya St., Vinnytsia, Ukraine,21008, e-mail: solona_o_v@ukr.net).

 

Annotation

The work investigates non-stationary oscillations of dissipative oscillators. The joint influence of resistance forces of different nature in the composition of the dissipative force on the oscillations of an elastic linear oscillator caused by its instantaneous loading by a constant external force is investigated. The work was limited to the case of small displacements, when the elastic characteristic of the system can be considered linear. The problem is nonlinear due to the account of the action of the dry friction force, but it allows the construction of exact analytical solutions in elementary functions. In this work, by the method of adding solutions, formulas are derived for calculating the amplitude of oscillations and the duration of half cycles. First, a variant is considered when the resistance force consists of linear viscous and dry friction forces. Then a generalization is made to the case of three resistance forces. The third force is the force of positional friction, which arises in elastic elements such as a leaf spring. It is shown that as a result of the action of the total resistance force, the oscillatory process of a loaded oscillator has a finite number of cycles and is limited in time, which is usually observed in practice. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. To check the adequacy of the derived calculation formulas, numerical computer integration of the nonlinear differential equations of the oscillator motion was additionally carried out.

The full agreement of the numerical results obtained using various methods is shown. In addition to direct problems of dynamics, the inverse problems of determining the characteristics of the load and resistance from the results of measuring the amplitude of oscillations are also considered. The derived calculation formulas are also suitable for identifying the characteristics of the load and resistance based on the results of experimental measurements of the oscillation ranges. Examples of identifying these characteristics are given.

The study showed that the nonlinear problem of motion of an instantly loaded oscillator with the total resistance of several forces of different nature has an analytical solution in elementary functions. The presence of such resistance significantly affects the motion of the oscillator after loading. The constructed analytical solutions give results such as the numerical integration of the original nonlinear differential equation on a computer, which confirms the adequacy of the formulas obtained.

 

Keywords: stepped power impulse, joint action of resistance forces of different nature, determination of vibration ranges, comparison of results, different methods, identification of load and resistance characteristics.

List of references

1. Mitropolskij, Yu. A. (2012). Izbrannye trudy : v 2 t [Selected works : in 2 vol.]. Kiev : Naukova dumka. [In Russian].

2. Goloskokov, E. G., & Filippov, A. P. (1971). Instationäre Schwingungen Mechanischer Systeme [Unsteady vibrations of mechanical systems]. Berlin : Academie-Verlag. [In German].

3. Olshanskiy, V. P., & Olshanskiy, S. V. (2014). Metod VBK v raschyotakh nestaczionarnykh kolebanij osczilyatorov. [VBK method in calculating non-stationary oscillations of oscillators]. Kharkov : Miskdruk. [In Russian].

4. Pysarenko, G. S., Kvitka, O. L., & Umanskyj, E. S. (2004) Opir materialiv [Strength of materials]. Kyiv : Vyshha shkola. [In Ukrainian].

5. Shkelov, L. T., Stankevych, A. M., & Poshyvak, D. V. (2011) Opir materialiv [Strength of materials]. Kyiv : Vipol. [In Ukrainian].

6. Olshanskiy, V. P., Tishhenko, L. N. & Olshanskiy, S. V. (2012). Kolebaniya sterzhnej i plastin pri mekhanicheskom udare. [Vibrations of the rods and plates under mechanical shock]. Kharkov : Miskdruk. [In Russian].

7. Panovko, Ya. G. (1977). Vvedenie v teoriyu mekhanicheskogo udara [Introduction to the theory of mechanical shock]. Moskva : Nauka. [In Russian].

8. Bolotin, V. V. (Ed) (1978) Vibraczii v tekhnike. Spravochnik v shesti tomakh. Kolebaniya linejnykh sistem [Vibrations in technology. Reference book in six volumes. Oscillations of linear systems]. (Vols. 1). Moskva : Mashinostroenie. [In Russian].

9. Babakov, I. M. (2004). Teoriya kolebanij [Oscillation theory]. Kiev : Naukova dumka. [In Russian].

10. Olshanskiy, V. P., Tishhenko, L. N. & Olshanskiy, S. V. (2016). Dynamika dysypatyvnyh oscylyatoriv. [Dynamics of dissipative oscillators]. Kharkiv : Miskdruk. [In Ukrainian].

11. Olshanskiy, V. P., Slipchenko, M. V., Spolnik, O. I., & Burlaka, V. V. (2020). Nelinijni kolyvannya dysypatyvnyh oscylyatoriv. [Nonlinear oscillations of dissipative oscillators]. Kharkiv : Miskdruk. [In Ukrainian].

12. Smetankina, N. V., Ugrimov, S. V., Shupikov, O. M., & Buzko, Ya. P. (2002). Dynamichnyj vidguk plastyn, yaki lezhat na pruzhnij osnovi [Dynamic response of plates that lie on an elastic base]. Visnik NTU «KhPI». Seriya: Tekhnologiyiyi v mashinobuduvanni [Bulletin of NTU "KhPI". Series: Technologies in mechanical engineering]. Kharkiv, 19, 68-72. [In Ukrainian].

13. Smetankina, N. V. (2011). Nestaczionarnoe deformirovanie, termouprugost i optimizacziya mnogoslojnykh plastin i cilindricheskikh obolochek [Nonstationary deformation, thermoelasticity and optimization of multilayer plates and cylindrical shells]. Kharkov : Miskdruk. [In Russian].

14. Biderman, V. L. (1980). Teoriya mekhanicheskikh kolebanij [Theory of mechanical oscillations]. Moskva : Vysshaya shkola. [In Russian].

15. Suryaninov, N. G., Dashhenko, A. F., & Belous, P. A. (2000). Teoreticheskie osnovy dinamiki mashin [Theoretical foundations of machine dynamics]. Odessa : OGPU. [In Russian].

16. Yanyutin, E. G., Yanchevskij, I. V., Voropaj, A. V., & Sharapata, A. S. (2004). Zadachi impulsnogo deformirovaniya elementov konstrukczij [Problems of impulse deformation of structural elements]. Kharkov : KhNADU. [In Russian].

17. Yanyutin, E. G., Voropaj, A. V., Povalyaev, S. I., & Yanchevskij, I. V. (2010). Identifikacziya zagruzok pri impul`snom deformirovanii tel. Chast 2. [Identification of loads during impulse deformation of bodies. Part 2]. Kharkov : KhNADU. [In Russian].

18. Voropaj, A. V. (2018). Integralnye uravneniya Volterra v nekorrektnykh zadachakh nestaczionarnogo deformirovaniya plastin [Volterra integral equations in ill-posed problems of unsteady deformation of plates]. Kharkov : KhNADU. [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, Russian, 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.