Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Filippov S. B., Kozlova A. S. The asymptotic analysis of free vibrations of a cylindrical shell joined with annular plates. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 138-149. DOI: 10.18500/1816-9791-2024-24-1-138-149, EDN: HACAYF

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: 
HACAYF

The asymptotic analysis of free vibrations of a cylindrical shell joined with annular plates

Autors: 
Filippov Sergei Borisovich, St. Petersburg State University
Kozlova Anastasiya S., St. Petersburg State University
Abstract: 

Low frequencies and vibration modes of a closed circular cylindrical shell joined with annular plates are obtained by means of asymptotic methods. Two types of vibrations, corresponding to narrow and wide plates, are analyzed. If the width of the ring is sufficiently small, then the vibration mode of the stiffened shell is similar to the mode of the shell without rings. For wide plates joined with a cylindrical shell the vibration mode is localized on the surface of the ring, and the cylindrical shell itself does not actually deform. In both cases the solution of a boundary value problem is searched in the form of the sum of slowly varying functions and edge effect integrals. For narrow plates as a first approximation we obtain a problem about vibrations of the beam supported by springs. For wide plates the problem is reduced to a problem about vibrations of a ring plate.

Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 23-21-00111, https://rscf.ru/project/23-21-00111/).
References: 
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Received: 
04.12.2023
Accepted: 
28.12.2023
Published: 
01.03.2024