Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

• 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
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-018-3690-7

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.