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Journal of Mathematical Sciences

, Volume 240, Issue 1, pp 98–112 | Cite as

Axially Symmetric Vibrations of Elastic Annular Bases and a Perfect Two-Layer Liquid in a Rigid Annular Cylindrical Vessel

  • Yu. М. Кononov
  • V. P. Shevchenko
  • Yu. O. Dzhukha
Article
  • 17 Downloads

We deduce a frequency equation for the natural coupled axially symmetric vibrations of elastic bases (in the form of annular plates) and a heavy two-layer incompressible perfect liquid in a rigid annular cylindrical vessel. We consider different limiting cases: the case of degeneration of annular plates into membranes, the case of absolutely rigid or circular plates, and the case of absence of the upper plate (liquid with free surface). For a broad range of parameters of the analyzed mechanical system, we investigate the frequency spectra and obtain a series of mechanical effects in the problem of hydroelasticity.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yu. М. Кononov
    • 1
  • V. P. Shevchenko
    • 1
  • Yu. O. Dzhukha
    • 1
  1. 1.Stus Donets’k National UniversityVinnytsyaUkraine

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