Natural Vibrations of Truncated Conical Shells Containing Fluid

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...

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Bibliographic Details
Published in:Mechanics of solids 2022-12, Vol.57 (8), p.1971-1986
Main Authors: Bochkarev, S. A., Lekomtsev, S. V., Matveenko, V. P.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Classical Mechanics
Compressible fluids
Conical shells
Differential equations
Euler-Lagrange equation
Exact solutions
Generalized differential quadrature method
Hydrodynamic pressure
Interpolation
Ordinary differential equations
Physics
Physics and Astronomy
Quadratures
Resonant frequencies
Shell theory
Spherical coordinates
Straight lines
Transformations (mathematics)
Wave equations
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Summary: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.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654422080064