Free Vibrations of a Cylindrical Shell Reinforced by an Elastic Annular Rib

We propose an algorithm for the evaluation of frequencies and forms of natural vibrations of a thin-walled circular cylindrical shell reinforced by a transverse annular elastic rib of small width with regard for the presence of discontinuities of the first kind in the force factors acting on the lin...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-07, Vol.274 (1), p.94-113
Main Authors: Trotsenko, V. A., Trotsenko, Yu. V.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Cylindrical shells
Elastic shells
Free vibration
Mathematics
Mathematics and Statistics
Ritz method
Vibration
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Summary:We propose an algorithm for the evaluation of frequencies and forms of natural vibrations of a thin-walled circular cylindrical shell reinforced by a transverse annular elastic rib of small width with regard for the presence of discontinuities of the first kind in the force factors acting on the line of contact of the rib with the shell. To construct approximate solutions of the analyzed spectral problem, we use the variational method in combination with the partition of the domain of definition of the required functions into regular subdomains in each of which the displacements, forces, and moments have the properties of continuity and differentiability. The Ritz method proposed for the solution of the analyzed problem guarantees convergence in the uniform metric for displacements and the force factors of elastic shell.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06573-0