Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-03, Vol.229 (4), p.470-486
Main Author: Trotsenko, Yu. V.
Format: Article
Language:English
Subjects:
ALGORITHMS
Analysis
APPROXIMATIONS
BOUNDARY CONDITIONS
Circular cylinders
Computational fluid dynamics
CYLINDERS
Elastic shells
ENGINEERING
EQUATIONS
EXACT SOLUTIONS
Free surfaces
HYDRODYNAMICS
Hydroelasticity
IDEAL FLOW
LIQUIDS
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
MECHANICAL VIBRATIONS
NUMERICAL ANALYSIS
Shells of revolution
VARIATIONAL METHODS
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Summary:We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3690-7