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: 
01.03.2024
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Russian
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Article
UDC: 
534.1:539.3
EDN: 
BFHZFQ

Free vibration frequencies of prismatic thin shells

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

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.

Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 23-21-00111, https://rscf.ru/project/23-21-00111/).
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Received: 
28.11.2023
Accepted: 
28.12.2023
Published: 
01.03.2024