Frequency energy function in dynamic states estimation of technical objects

DOI: 10.34759/trd-2021-118-04

Аuthors

Eliseev A. V.^1*, Kuznetsov N. K.^1**, Eliseev S. V.^2***

1. Irkutsk National Research Technical University, 83, Lermontov str., Irkutsk, 664074, Russia
2. Irkutsk State Transport University (IrGUPS), 15, Chernyshevsky str., Irkutsk, 664074, Russia

*e-mail: eavsh@ya.ru
**e-mail: knik@istu.edu
***e-mail: eliseev_s@inbox.ru

Abstract

The article proposes a new approach to the dynamic properties evaluation of mechanical oscillatory systems, as calculation schemes for technical objects operating in modes of intense vibration loading.

The purpose of the study consists in developing ideas of employing frequency energy functions representing potential and kinetic energies ratio in a specific form based on the application of relations of coordinates in the free oscillations mode.

Technologies of system analysis and structural mathematical modelling, within which framework the block diagram of the equivalent in dynamic sense automatic control system is being correlated in mechanical oscillatory system, are used.

The article demonstrates that the design schemes of technical objects, represented by design schemes in the form of mechanical oscillatory systems, allow detailing perception about systems’ dynamic properties, associated with the objects’ dynamic state, defined by the spectrum of natural vibration frequencies in a wide range. Growing attention to the reliability ensuring and operation safety of machines and equipment predetermines the attention to the frequency properties of the systems and accounting for the specifics of theif formation and manifestation.

The authors propose a method for dynamic properties evaluation of mechanical oscillatory systems based on the frequency energy function, which allows determining the frequencies of natural oscillations and their dependences on the system parameters, depending on the so-called cohesiveness coefficient of amplitudes by the coordinates of the system.

Keywords:

mechanical oscillatory systems, block diagrams, frequency energy function, transfer function, inter-partial bonds, frequency characteristics

References

1. De Silva C.W. Vibration. Fundamentals and Practice, Boca Raton, London, New York, Washington, D.C., CRC Press, 2000, 957 p.

2. Karnovsky I.A., Lebed E. Theory of Vibration Protection, Springer International Publishing, Switzerland, 2016, 708 p.

3. Eliseev S.V., Eliseev A.V. Theory of Oscillations. Structural Mathematical Modeling in Problems of Dynamics of Technical Objects. Series: Studies in Systems, Decision and Control, vol. 252, Springer International Publishing, Cham, 2020, 521 p.

4. Betkovskii Yu.Ya., Sidorenko A.S. Trudy MAI, 2007, no. 29. URL: http://trudymai.ru/eng/published.php?ID=33978

5. Popov I.P. Trudy MAI, 2020, no. 115. URL: http://trudymai.ru/eng/published.php?ID=119888. DOI: 10.34759/trd-2020-115-01

6. Il’inskii V.S. Zashchita apparatov ot dinamicheskikh vozdeistvii (Devices protection from dynamic excitations), Moscow, Energiya, 1970, 320 p.

7. Ivovich V.A., Onishchenko V.Ya. Zashchita ot vibratsii v mashinostroenii (Vibration protection in mechanical engineering), Moscow, Mashinostroenie, 1990, 271 p.

8. Kolovskii M.Z. Avtomaticheskoe upravlenie vibrozashchitnymi sistemami (Automatic control of vibration protection systems), Moscow, Nauka, 1976, 320 p.

9. Korenev B.G., Reznikov L.M. Dinamicheskie gasiteli kolebanii. Teoriya i tekhnicheskie prilozheniya (Dynamic vibration dampers. Theory and technical applications), Moscow, Nauka, 1988, 304 p.

10. Krasil’nikov P.S., Storozhkina T.A. Trudy MAI, 2011, no. 46. URL: http://trudymai.ru/eng/published.php?ID=26045

11. Eliseev S.V., Khomenko A.P. Dinamicheskoe gashenie kolebanii: kontseptsiya obratnoi svyazi i strukturnye metody matematicheskogo modelirovaniya (Dynamic vibration damping: feedback concept and structural methods of mathematical modeling), Novosibirsk, Nauka, 2014, 357 p.

12. Eliseev S.V. Prikladnoi sistemnyi analiz i strukturnoe matematicheskoe modelirovanie (dinamika transportnykh i tekhnologicheskikh mashin: svyaznost’ dvizhenii, vibratsionnye vzaimodeistviya, rychazhnye svyazi): monografiya (Applied system analysis and structural mathematical modeling (dynamics of transport and technological machines: connectivity of movements, vibration interactions, lever bonds)), Irkutsk, IrGUPS, 2018, 692 p.

13. Popov I.P. Trudy MAI, 2021, no. 116. URL: http://trudymai.ru/eng/published.php?ID=121007. DOI: 10.34759/trd-2021-116-01

14. Kuznetsov N.K. Dinamika upravlyaemykh mashin s dopolnitel’nymi svyazyami (Dynamics of controlled machines with additional connections), Irkutsk, IRGTU, 2009, 290 p.

15. Bol’shakov R.S. Osobennosti vibratsionnykh sostoyanii transportnykh i tekhnologicheskikh mashin. Dinamicheskie reaktsii i formy vzaimodeistviya elementov (Vibration states specifics of transportation technological machines. Dynamic reactions and forms of elements interaction), Novosibirsk, Nauka, 2020, 411 p.

16. Ganiev R.F., Kononenko V.O. Kolebaniya tverdykh tel (Vibrations of solids), Moscow, Nauka, 1976, 432 p.

17. Chelomei V.N. Vibratsii v tekhnike. Kolebaniya lineinykh system (Vibrations in technology. Oscillations of linear systems), Moscow, Mashinostroenie, 1978, 352 p.

18. Harris S.M., Srede C.E. Shock and Vibration Handbook, New York, McGraw, Hill Book So, 2002, 1457 p.

19. Relei D.V. Teoriya zvuka (Theory of Sound), Moscow-Leningrad, Gostekhteoretizdat, 1940, vol. 1, 500 p.

20. Lur’e A.I. Operatsionnoe ischislenie i primenenie v tekhnicheskikh prilozheniyakh (Operational calculus and its application in technical applications), Moscow, Nauka, 1959, 368 p.

    
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