Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2022-8pp.1971-1986

Archive of Issues

Total articles in the database: 12854
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4810

<< Previous article | Volume 57, Issue 8 / 2022 | Next article >>
S.A. Bochkarev, S.V. Lekomtsev, and V.P. Matveenko, "Natural Vibrations of Truncated Conical Shells Containing Fluid," Mech. Solids. 57 (8), 1971-1986 (2022)
Year 2022 Volume 57 Number 8 Pages 1971-1986
DOI 10.3103/S0025654422080064
Title Natural Vibrations of Truncated Conical Shells Containing Fluid
Author(s) S.A. Bochkarev (Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia, bochkarev@icmm.ru)
S.V. Lekomtsev (Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia, lekomtsev@icmm.ru)
V.P. Matveenko (Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia, mvp@icmm.ru)
Abstract The article presents the results of studies on the natural vibration frequencies of circular truncated conical shells completely filled with an ideal compressible fluid. The behavior of the elastic structure is described in the framework of classical shell theory, the equations of which are written in the form of a system of ordinary differential equations with respect to new unknowns. Small fluid vibrations are described by the linearized Euler equations, which in the acoustic approximation are reduced to the wave equation with respect to hydrodynamic pressure and written in spherical coordinates. Its transformation to the system of ordinary differential equations is performed in three ways: by the straight line method, by spline interpolation and by the method of differential quadrature. The formulated boundary value problem is solved using the Godunov orthogonal sweep method. The calculation of natural frequencies of vibrations is based on the application of a stepwise procedure and subsequent refinement by the half-division method. The validity of the results obtained is confirmed by their comparison with known numerical-analytical solutions. The efficiency of frequency calculations in the case of using different methods of wave equation transformation is evaluated for shells with different combinations of boundary conditions and cone angles. It is demonstrated that the use of the generalized differential quadrature method provides the most cost-effective solution to the problem with acceptable calculation accuracy.
Keywords classical shell theory, conical shell, Godunov’s orthogonal sweep method, natural vibrations, ideal compressible fluid, method of lines, cubic spline, differential quadrature method
Received 03 March 2022Revised 03 May 2022Accepted 15 May 2022
Link to Fulltext
<< Previous article | Volume 57, Issue 8 / 2022 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100