Investigation of free oscillations of the spherical shell containing a liquid by the inverse method

Authors

  • Гюльдаста Акиф кызы Мамедова Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Republic of Azerbaijan, Baku, st. B.Vahabzade 9. AZ1141, Azerbaijan
  • Мехсети Акиф кызы Рустамова Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Republic of Azerbaijan, Baku, st. B.Vahabzade 9. AZ1141, Azerbaijan
  • Самир Рамиз оглы Агасиев Azerbaijan Architecture and Construction University, Republic of Azerbaijan, Baku, st. Ayna Sultanova 5. AZ1141, Azerbaijan

DOI:

https://doi.org/10.15587/1729-4061.2013.19422

Keywords:

oscillations, wave, frequency, density, shell, pressure, potential

Abstract

The problems of free oscillations of shells, contacting with the continuous medium are considered in the known works of various authors. As a rule, the problems are reduced to the transcendental equations or the systems the solution of which by analytical methods is not possible. The results of the investigation are presented in the form of tables or graphs, obtained by numerical methods. The problem of axisymmetric free oscillations of elastic thin-walled spherical shell, containing a compressible liquid is considered in the paper. Herewith, the equations of motion are constructed in radial motions and with the use of special potential. The problem is reduced to the investigation of the homogeneous system of two equations with respect to the radial motion and the mentioned potential. The condition of non-triviality of the system solution leads to the transcendental equation. In the known works, the solution of the specified transcendental equations is found by numerical methods. The analytical solution, binding the frequency of the system shell - liquid with the frequency of the shell without the liquid is constructed by the inverse method. This solution allows to investigate the phenomenon of the analytical method and to build the frequency spectra.

The potential motion both of shell and liquid is considered. The equation of the shell motion in special potentials is used. The liquid motion equation is represented by the wave equation. The liquid motion is proposed as non-separable.

Author Biographies

Гюльдаста Акиф кызы Мамедова, Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Republic of Azerbaijan, Baku, st. B.Vahabzade 9. AZ1141

Candidate of Physics and Mathematics Sciences, docent

Department: Wave dynamics

Мехсети Акиф кызы Рустамова, Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Republic of Azerbaijan, Baku, st. B.Vahabzade 9. AZ1141

Candidate of Physics and Mathematics Sciences, docent

Department: Wave dynamics

Самир Рамиз оглы Агасиев, Azerbaijan Architecture and Construction University, Republic of Azerbaijan, Baku, st. Ayna Sultanova 5. AZ1141

Candidate for a degree

Department:"Operation and reconstruction of structures and buildings

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Published

2013-12-12

How to Cite

Мамедова, Г. А. к., Рустамова, М. А. к., & Агасиев, С. Р. о. (2013). Investigation of free oscillations of the spherical shell containing a liquid by the inverse method. Eastern-European Journal of Enterprise Technologies, 6(7(66), 16–19. https://doi.org/10.15587/1729-4061.2013.19422

Issue

Vol. 6 No. 7(66) (2013): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2014 Гюльдаста Акиф кызы Мамедова, Мехсети Акиф кызы Рустамова, Самир Рамиз оглы Агасиев

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