Calculation studies of the dynamic characteristics of spherical and toroidal shells

  • S. P. Gavelya
  • N. I. Kononenko


An algorithm for the calculation of natural vibrations and waves, based on the use of special matrices belonging to the type of the Green matrices (according to the procedure [1]), is realized in this work. Results of calculations for a spherical shell and a toroidal shell are presented and discussed. The frequencies and modes of natural frequencies of gradually increasing tones are demonstrated. The data obtained are used for the calculation of propagating waves for various methods of initial perturbation. Specific features of the distribution of dynamic stresses are discovered.


Mathematical Modeling Mechanical Engineer Industrial Mathematic Dynamic Characteristic Spherical Shell 
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Literature cited

  1. 1.
    S. P. Gavelya, “The calculation of the stress-strain state of a toroidal shell with a hole,” Prikl. Mekhan.,9, No. 2 (1972).Google Scholar
  2. 2.
    I. A. Meerovich, “An approximate method of determining the frequencies of natural vibrations of cylindrical, conical, and toroidal shells,” in: Strength and Dynamics of Aero-Engines [in Russian], No. 2, Mashinostroenie, Moscow (1965).Google Scholar
  3. 3.
    S. P. Gavelya and N. I. Kononenko, “Use of Green's functions when investigating natural vibrations of two-dimensional constructions,” in: Computational and Applied Mathematics [in Russian], No. 18, Izd. Kievsk. Un-ta., Kiev (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • S. P. Gavelya
    • 1
  • N. I. Kononenko
    • 1
  1. 1.Dnepropetrovsk

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