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Natural Vibrations of a Cylindrical Shell with an End Cap. I. Asymptotic Analysis

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Abstract

The low eigenfrequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap in the form of a shallow spherical segment attached to it are investigated using numerical and asymptotic methods. Three types of natural vibrations of the structure are distinguished. The eigenfrequencies and vibration modes of the first type are close to the frequencies and vibration modes of a shallow spherical shell, the modes and frequencies of the second type, to the frequencies and modes of a cylindrical shell, and the third type, to the frequencies and vibration modes of a cantilever beam with a load at the end. In this article, approximate values for the frequencies of vibrations of the first type are found using asymptotic methods. Asymptotic and numerical results obtained using the finite-element method are in good agreement.

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Funding

This paper was funded by Russian Science Foundation (grant 23-21-00111): https://rscf.ru/en/project/23-21-00111/

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Authors and Affiliations

  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    S. B. Filippov, A. L. Smirnov & G. A. Nesterchuk

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  1. S. B. Filippov
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  2. A. L. Smirnov
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  3. G. A. Nesterchuk
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Corresponding authors

Correspondence to S. B. Filippov, A. L. Smirnov or G. A. Nesterchuk.

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Translated by O. Pismenov

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Filippov, S.B., Smirnov, A.L. & Nesterchuk, G.A. Natural Vibrations of a Cylindrical Shell with an End Cap. I. Asymptotic Analysis. Vestnik St.Petersb. Univ.Math. 56, 84–92 (2023). https://doi.org/10.1134/S1063454123010065

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