Construction of solutions for the problem of free oscillations of an ideal liquid in cavities of complex geometric form
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We consider the problem of free oscillations of an ideal incompressible liquid in cavities of complex geometric form. The domain filled with liquid is divided into subdomains of simpler geometric form. The original problem is reduced to the spectral problem for a part of the domain filled with liquid. To this end, we use solutions of auxiliary boundary-value problems in subdomains. We construct approximate solutions of the problem obtained using the variational method. We also consider the problem of the rational choice of a system of coordinate functions. Results of the numerical realization of the proposed method are presented.
KeywordsApproximate Solution Variational Method Original Problem Rational Choice Spectral Problem
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- 2.N. N. Moiseev and A. A. Petrov, Numerical Methods for the Calculation of Eigenfrequencies of Oscillations of a Bounded Volume of Liquid [in Russian], Izd. VTs AN SSSR, Moscow (1966).Google Scholar
- 3.N. N. Moiseev (editor), Variational Methods in Problems of Oscillations of a Liquid and a Body with Liquid [in Russian], Izd. VTs AN SSSR, Moscow (1962).Google Scholar
- 4.S. F. Feshchenko, I. A. Lukovskii, B. I. Rabinovich, and L. V. Dokuchaev, Methods for Determination of Attached Masses of Liquid in Movable Cavities [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
- 5.N. D. Kopachevskii, S. N. Krein, and Ngo Zuy Kan, Operator Methods in Linear Hydrodynamics [in Russian], Nauka, Moscow (1989).Google Scholar
- 7.S. T. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).Google Scholar
- 8.I. A. Lukovskii, M. Ya. Barnyak, and A. N. Komarenko, Approximate Methods for the Solution of Problems of Dynamics of a Bounded Volume of Liquid [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
- 10.I. O. Lukovs’kyi and M. Ya. Barnyak, “Approximate method for the construction of solutions of the problem of free oscillations of an ideal liquid in a skew circular cylinder,” Dopov. Nats. Akad. Nauk Ukr., No. 5, 28–32 (1997).Google Scholar