Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Dzebisashvili G. T., Smirnov A. L., Filippov S. B. Free vibration frequencies of prismatic thin shells. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 49-56. DOI: 10.18500/1816-9791-2024-24-1-49-56, EDN: BFHZFQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 217)
Article type: 

Free vibration frequencies of prismatic thin shells

Dzebisashvili Georgii Tamazovich, St. Petersburg State University
Smirnov Andrei L., St. Petersburg State University
Filippov Sergei Borisovich, St. Petersburg State University

The paper examines the natural frequencies of prismatic thin shells, the cross-section of which is the regular polygon. Spectra of free vibration frequencies of such shells are analyzed as the number of cross-section sides increases, provided that the perimeter is preserved. The relation between fundamental frequencies of the prismatic shells with the regular polygonal cross-section and a circular cylindrical shell is discussed. For a small and large number of polygon sides analytical and asymptotic solutions are compared with numerical solutions obtained by the finite element method (COMSOL). The convergence of the numerical method is studied for the prismatic shell with a large number of facets.

This work was supported by the Russian Science Foundation (project No. 23-21-00111, https://rscf.ru/project/23-21-00111/).
  1. Filippov S. B., Haseganu E. M., Smirnov A. L. Free vibrations of square elastic tubes with a free end. Mechanics Research Communications, 2000, vol. 27, iss. 4, pp. 457–464. https://doi.org/10.1016/S0093-6413(00)00118-X, EDN: LGGAGP
  2. Dzebisashvili G. T. Free vibrations of cylindrical shells with the square cross-section. Trudy seminara “Komp’yuternye metody v mekhanike sploshnoy sredy” 2017–2018 [Proceedings of the seminar “Computer methods in continuum mechanics” 2017–2018]. St. Petersburg, St. Petersburg State University Publ., 2019, pp. 13–29 (in Russian). EDN: VMRBFC
  3. Amosov A. S. Free vibrations of a thin rectangular elastic tube. Vestnik Sankt-Peterburgskogo Universiteta. Matematika. Mekhanika. Astronomiya [Bulletin of St. Petersburg University. Mathematics. Mechanics. Astronomy], 2004, iss. 1, pp. 67–72 (in Russian). EDN: RTSPCN
  4. Chen Y., Jin G., Liu Z. Free vibration of a thin shell structure of rectangular cross-section. Key Engineering Materials, 2011, vol. 486, pp. 107–110. https://doi.org/10.4028/www.scientific.net/KEM.486.107
  5. Dzebisashvili G. T., Filippov S. B. Vibrations of cylindrical shells with rectangular cross-section. Journal of Physics: Conference Series, 2020, vol. 1479. Available at: https://iopscience.iop.org/article/10.1088/1742-6596/1479/1/012129/pdf (accessed February 26, 2021).
  6. Goncalves R., Camotim D. The vibration behaviour of thin-walled regular polygonal tubes. Thin-Walled Structures, 2014, vol. 84, pp. 177–188. https://doi.org/10.1016/j.tws.2014.06.011
  7. Krajcinovic D. Vibrations of prismatic shells with hexagonal cross section. Nuclear Engineering and Design, 1972, vol. 22, iss. 1, pp. 51–62. https://doi.org/10.1016/0029-5493(72)90061-1
  8. Borkovic A., Kovacevic S., Milasinovic D. D., Radenkovic G., Mijatovic O., Golubovic-Bugarski V. Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method. Thin-Walled Structures, 2017, vol. 117, pp. 63–88. https://doi.org/10.1016/j.tws.2017.03.033
  9. Liang S., Chen H. L., Liang T. X. An analytical investigation of free vibration for a thin-walled regular polygonal prismatic shell with simply supported odd/even number of sides. Journal of Sound and Vibration, 2005, vol. 284, iss. 1–2, pp. 520–530. https://doi.org/10.1016/j.jsv.2004.08.011
  10. Leissa A. W. Vibration of Plates. Washington, US Government Printing Office, 1969. 353 p.
  11. Goldenweiser A. L., Lidsky V. B., Tovstik P. E. Svobodnye kolebaniya tonkikh uprugikh obolochek [Free Vibrations of Thin Elastic Shells]. Moscow, Nauka, 1979. 384 p. (in Russian).