Modeling vibrations of a thin-walled cylindrical shell under uniform temperature impact at a variation formulation of the problem

DOI: 10.34759/trd-2021-117-03


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

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



The purpose of the article consists in verifying mathematical model of thin-walled cylindrical shell vibrations under the impact of the uniform temperature based on variation formulation, and employing various methods, including the experimental one.

The state-of-the-art construction often employs expressive and cost-effective shapes of buildings and structures in the form of thin-walled cylindrical shells. These buildings herewith are being exposed to temperature impacts and external forces action, leading to technogenic accidents. To avoid these accidents, frequency responce of buildings and structures should be computed. Dynamic temperature variations of the shell lead to the elastic modulus of buildings changing, which affects the frequency response dynamics. The existing vibration analysis models for thin-walled cylindrical shells do not fully account for this fact, thus, improved analytical models development is required with confirmation of the high quality of the developed model. Experimental verification is one of the most common methods of mathematical models proofing. The new theoretical basis parameters are being verified with a realistic scaled-down model of the structure, and comparison of experimental and theoretical data is being performed.

The article presents a new design model for thin-walled cylindrical structures vibrations being exposed to the uniform heating, based on variation formulation. The obtained design model has been verified by experiment, and its application range has been determined.

The new verified mathematical model can be used for performing structural analysis, in design bureaus conducting vibration analysis for cylindrical shells.

Comparison of experimental and theoretical results of was performed. Convergence of the results is less than 5%. It was demonstrated also that the experimental data revealed a discrepancy with the results obtained while vibrations computing of the open cylindrical shells by the well-known mathematical model.


thin-walled cylindrical shell, forced vibrations, design model, experimental research, variation formulation of the problem


  1. Vlasov V.Z. Obshchaya teoriya obolochek i ee prilozhenie v tekhnike (General theory of shells and its application in technology), Moscow-Leningrad, Gostekhizdat, 1949, 784 p.

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

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

  4. Sysoev O.E., Dobryshkin A.Yu., Nein Sit Naing. Trudy MAI, 2018, no. 98. URL:

  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., Dobrychkin A.Yu., Nyein Sitt Naing, Baenkhaev A.V. 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/

  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. Sysoev O.E., Dobrychkin A.Yu., Nyein Sitt Naing. Nonlinear Oscillations of Elastic Curved plate carried to the associated masses system, IOP Conference Series: Materials Science and Engineering, 2017, vol. 262. DOI: 10.1088/1757-899X/262/1/012055
  9. 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.

  10. Y. Qu, H. Hua, and G. Meng. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 2013, vol. 95, pp. 307 – 321.

  11. Y. Xing, B. Liu, and T. Xu. Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions, International Journal of Mechanical Sciences, 2013, vol. 75, pp. 178 – 188.

  12. M. Chen, K. Xie, W. Jia, and K. Xu. Free and forced vibration of ring-stiffened conical—cylindrical shells with arbitrary boundary conditions, Ocean Engineering, 2015, vol. 108, pp. 241 – 256.

  13. H. Li, M. Zhu, Z. Xu, Z. Wang, and B. Wen. The influence on modal parameters of thin cylindrical shell under bolt looseness boundary, Shock and Vibration, 2016. DOI:

  14. Foster N., Fernández–Galiano L. Norman Foster in the 21st Century, Monografías, Artes Gráficas Palermo, 2014, 328 p.

  15. 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.

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

  17. Belostochnyi G.N., Myl’tsina O.A. Trudy MAI, 2015, no. 82. URL:

  18. Kuznetsova E.L., Tarlakovskii D.V., Fedotenkov G.V., Medvedskii A.L. Trudy MAI, 2013, no. 71. URL:

  19. 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.

  20. Nushtaev D.V., Zhavoronok S.I., Klyshnikov K.Yu., Ovcharenko E.A. Trudy MAI, 2015, no. 82. URL:

  21. Grushenkova E.D., Mogilevich L.I., Popov V.S., Popova A.A. Trudy MAI, 2019, no. 106. URL:

Download — informational site MAI

Copyright © 2000-2022 by MAI