Natural vibrations of a cylindrical shell with the end cap. II. Analysis of the spectrum

Authors

  • Grigory A. Nesterchuk St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Andrei L. Smirnov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Sergei B. Filippov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.213

Abstract

Using numerical and asymptotic methods, the lowest natural frequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it, having the shape of a shallow spherical segment, are studied in the paper. Three types of natural vibrations of the structure are described. Eigenfrequencies and modes of vibrations of the first type, close to the frequencies and modes of vibrations of a shallow spherical shell, were studied in previous works. In this paper, we study the forms and frequencies of the second type of vibrations (cylindrical shell) and the third type (cantilever beam with the load). An optimization problem is solved to determine the values of the structure parameters, the relative thickness of its elements and the curvature of the end cap, at which the minimum value of the natural frequency is maximum. A comparison of the asymptotic and numerical results reveals their good agreement.

Keywords:

joint thin shells, free vibrations, asymptotic methods, optimization

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References

Литература

1. Нестерчук Г. А., Смирнов А. Л., Филиппов С. Б. Собственные колебания цилиндрическойоболочки с крышкой. I. Асимптотическийанализ. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 10 (68), вып. 1, 109-120 (2023). https://doi.org/10.21638/spbu01.2023.110

2. Филиппов С. Б. Теория сопряженныхи подкрепленныхоболочек. Санкт-Петербург, Изд-во С.-Петерб. ун-та (1999).

3. Гольденвейзер А. Л., Лидский В. Б., Товстик П. Е. Свободные колебания тонкихупругих оболочек. Москва, Наука (1979).

4. Timoshenko S. Vibration problems in engineering. New York, Van Nostrand (1955).

References

1. Nesterchuk G. A., Smirnov A. L., Filippov S. B. Natural vibrations of a cylindrical shell with the end cap. I. Asymptotic analysis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 10 (68), iss. 1, 109-120 (2023). https://doi.org/10.21638/spbu01.2023.110 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 56, iss. 1, XXX-XXX, (2023) (in print)]

2. Filippov S. B. The theory of conjugated and reinforced shells. St Petersburg, St Petersburg University Press (1999). (In Russian)

3. Goldenveizer A. L., Lidsky V. B., Tovstik P. E. Free Vibrations of Thin Elastic Shells. Moscow, Nauka Publ. (1979). (In Russian)

4. Timoshenko S. Vibration problems in engineering. Van Nostrand, New York (1955).

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Published

2023-05-10

How to Cite

Nesterchuk, G. A., Smirnov, A. L., & Filippov, S. B. (2023). Natural vibrations of a cylindrical shell with the end cap. II. Analysis of the spectrum. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 334–343. https://doi.org/10.21638/spbu01.2023.213

Issue

Vol. 10 No. 2 (2023)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.