 | | 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 |
Archive of Issues
| Total articles in the database: | | 12804 |
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| In English (Mech. Solids): | | 4760 |
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| 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 2022 | Revised |
03 May 2022 | Accepted |
15 May 2022 |
| Link to Fulltext |
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