Experimental verification of the mathematical model of free vibrations of a plate with rigidly clamped edges


Аuthors

Dobryshkin A. Y.*, Sysoev O. E.**, Sysoev E. O.**

Komsomolsk-na-Amure State University, 27, Lenina str., Komsomolsk-on-Amur, 681013, Russia

*e-mail: wwwartem21@mail.ru
**e-mail: fks@knastu.ru

Abstract

The article considers the results of experimental studies on testing a new mathematical model of a thin-walled plate with rigidly clamped edges free oscillations. As of today, plate designs with rigidly fixed edges are widely employed in aircraft building and construction structures: buildings and structures, as well as in various industries. At the same time, these structures are subjected to various loads (wind, snow, and vibration), which cause free vibrations and lead to resonance phenomena, in some cases, structural failure and technogenic disasters. Experimental studies today is one of the most effective. The external forces impact on the shell allows obtaining experimental dependences of the frequency response of the shell vibrations and the value of the attached mass with the test bench. The study of plate free vibrations allows studying the resonant vibration modes, the parameters of their onset, prevent destruction of the real shell structures. Vibrations with moderate amplitudes of free oscillations were decomposed according to the obtained equations. Verification of the discrete nonlinear oscillations model of the thin shell pinched at the edges, obtained during the research, was conducted using the multi-scale method. When performing experimental studies, a non-contact frequency response meter of the HSV-2000 system was applied. It consists of the HSV2001/2002 controller, HSV-800 laser unit and the rugged compact HSV-700 sensor head. The laser unit contains the interferometer and the low-power laser, as well as the Rohde & Schwarz RTB2002 oscilloscope. Based on the results of the research, experimental verification of the free oscillations mathematical model of a plate with rigidly clamped edges was performed. The results of the work allowed describing the dependence of the first eigenvalue λ on ε for the recursive formulation of the perturbation theory and the Padé approximation, as well as experimental data. The limiting value of the ε parameter, at which the difference in the results obtained by the recursive formulation of the perturbation theory and the Padé approximation will be within 5%, is ε = 0.4.

Keywords:

plate, rigid fixing, free vibrations

References

  1. Kubenko V.D., Koval’chuk P.S., Krasnopol’skaya T.S. Nelineinoe vzaimodeistvie form izgibnykh kolebanii tsilindricheskikh obolochek (Nonlinear interaction of shapes of cylindrical shells bending vibrations), Kiev, Naukova dumka, 1984, 220 p.

  2. Antuf’ev B.A. Kolebaniya neodnorodnykh tonkostennykh konstruktsii (Oscillations of inhomogeneous thin-walled structures), Moscow, Izd-vo MAI, 2011, 176 p.

  3. Sysoev O.E., Dobryshkin A.Yu., Nein Sit Naing. Trudy MAI, 2018, no. 98. URL: http://trudymai.ru/eng/published.php?ID=90079

  4. Guseva Zh.I. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 4 (52), pp. 99-104. DOI: 10.17084/20764359-2021-52-99

  5. Z. Wang, Q. Han, D. H. Nash, P. Liu. Investigation on inconsistency of theoretical solution of thermal buckling critical temperature rise for cylindrical shell, Thin-Walled Structures, 2017, no. 119, pp. 438-446. DOI: 10.1016/j.tws.2017.07.002

  6. Sysoev O.E., Dobryshkin A.Y., Nyein Sitt Naing et al. Investigation to the location influence of the unified mass on the formed vibrations of a thin containing extended shell, Materials Science Forum, 2019, vol. 945, pp. 885-892. DOI: 10.4028/www.scientific.net/MSF.945.885

  7. Sysoev O.E., Dobrychkin A.Yu. Natural vibration of a thin desing with an added mass as the vibrations of a cylindrical shell and curved batten, Journal of Heilongjiang university of science and technology, 2018, vol. 28, no. 1, pp.75—78.

  8. Y. Qu, Y. Chen, X. Long, H. Hua, and G. Meng. Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method, Applied Acoustics, 2013, vol. 74, no. 3, pp. 425-439. DOI: 10.1016/J.APACOUST.2012.09.002

  9. Foster N., Fernández-Galiano L. Norman Foster: in the 21st Century, AV, Monografías, Artes Gráficas Palermo, 2013, pp. 163–164.

  10. Eliseev V.V., Moskalets A.A., Oborin E.A. One-dimensional models in turbine blades dynamics, Lecture Notes in Mechanical Engineering, 2016, vol. 9, pp. 93-104. DOI: 10.1007/978-3-319-29579-4_10

  11. Belostochnyi G.N., Myl’tsina O.A. Trudy MAI, 2015, no. 82. URL: http://trudymai.ru/eng/published.php?ID=58524

  12. Kuznetsova E.L., Tarlakovskii D.V., Fedotenkov G.V., Medvedskii A.L. Trudy MAI, 2013, no. 71. URL: http://trudymai.ru/eng/published.php?ID=46621

  13. Feoktistov S.I. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 1 (49), pp. 76-82. DOI: 10.17084/20764359_2021_49_76

  14. Kanashin I.V., Grigor’eva A.L., Khromov A.I., Grigor’ev Yan.Yu., Mashevskii V.A. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 3 (51), pp. 39-41. DOI: 10.17084/20764359-2021-51-39

  15. Demin A.A., Golubeva T.N., Demina A.S. The program complex for research of fluctuations’ ranges of plates and shells in magnetic field, 11th Students’ Science Conference «Future Information technology solutions», Bedlewo, 3-6 October 2013, pp. 61-66.

  16. Nushtaev D.V., Zhavoronok S.I., Klyshnikov K.Yu., Ovcharenko E.A. Trudy MAI, 2015, no. 82, URL: http://trudymai.ru/eng/published.php?ID=58589

  17. Grushenkova E.D., Mogilevich L.I., Popov V.S., Popova A.A. Trudy MAI, 2019, no. 106. URL: http://trudymai.ru/eng/published.php?ID=105618

  18. Hautsch N., Okhrin O., Ristig A. Efficient iterative maximum likelihood estimation of highparameterized time series models, Berlin, Humboldt University, 2014, 34 p.

  19. Sablin P.A., Shchetinin V.S. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 3 (51), pp. 104-106. DOI: 10.17084/20764359-2021-51-104

  20. Andrianov I.K. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 3 (51), pp. 14-20. DOI: 10.17084/20764359-2021-51-14

  21. Ivankova E.P. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2021, no. 3 (51), pp. 85-89. DOI: 10.17084/20764359-2021-51-85

  22. Evstigneev A.I., Dmitriev E.A., Odinokov V.I., Ivankova E.P., Usanov G.I., Petrov V.V. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2020, no. 7 (47), pp. 104-107.


Download

mai.ru — informational site MAI

Copyright © 2000-2024 by MAI

 Вход