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
The asymptotic analysis of free vibrations of a cylindrical shell joined with annular plates
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.
- Filippov S. B. Teoriya sopryazhennykh i podkreplennykh obolochek [Theory of Joint and Stiffened Shells]. St. Petersburg, St. Petersburg State University Press, 1999. 196 p. (in Russian).
- Filippov S. B. Asymptotic approximations for frequencies and vibration modes of cylindrical shell stiffened by annular plates. Analysis of Shells, Plates, and Beams – A State of the Art Report. Springer’s Series Advanced Structured Materials, vol. 123. 2020, pp. 123–140. https://doi.org/10.1007/978-3-030-47491-1_7
- Gol’denveizer A. L., Lidskii V. B., Tovstik P. E. Svobodnye kolebaniya tonkikh uprugikh obolochek [Free Vibrations of Thin Elastic Shells]. Moscow, Nauka, 1979. 384 p. (in Russian).
- Bauer S. M., Filippov S. B., Smirnov A. L., Tovstik P. E., Vaillancourt R. Asymptotic Methods in Mechanics of Solids. International Series of Numerical Mathematics, vol. 167. Springer International Publishing, Switzerland, 2015. 325 p.
- Filippov S. B. Optimal design of stiffened cylindrical shells based on an asymptotic approach. Technishe Mechanik, 2004, vol. 24, iss. 3–4, pp. 221–230. https://journals.ub.ovgu.de/index.php/techmech/article/view/927
- Bolotin V. V. (ed.) Vibratsii v tekhnike [Vibrations in Technique]. Vol. 1. Moscow, Mashinostroenie Publishers, 1978. 352 p. (in Russian). 7.
- Timoshenko S. P., Donovan H. Y., Uiver U. Kolebaniya v inzhenernom dele [Vibration Problems in Engineering]. Moscow, Mashinostroenie Publishers, 1985. 472 p. (in Russian).
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