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Sloshing frequencies

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Abstract

The sloshing problem is a linear eigenvalue problem for a partial differential operator that describes the small lateral oscillations of the free surface of an ideal fluid on a container subject to gravity. We consider two-dimensional problems on regions representing the cross-section of a cylindrical tank or canal. A conformal mapping transforms the sloshing problem on the given region to a weighted eigenvalue problem on a simple region such as a rectangle. The weighted problem can be treated very effectively by the powerful methods of intermediate problems. The strength and versatility of the method is illustrated with a variety of examples.

Zusammenfassung

Das Schlingerproblem ist ein lineares Eigenwertproblem für einen partiellen Differentialoperator, das die kleinen seitlichen Schwingungen der freien Oberfläche einer idealen Flüssigkeit in einem gewichtsbelasteten Behälter beschreibt. Wir betrachten zweidimensionale Schlingerprobleme im Querschnitt eines zylindrischen Behälters bzw. Kanals. Eine konforme Abbildung verwandelt das Schwingungsproblem auf dem gegebenen Gebiete in ein gewichtetes Eigenwertproblem in einem einfacheren Gebiete, z. B. in einem Rechteck. Das transformierte Problem kann dann leicht durch die Methode der Zwischenprobleme (Weinstein) behandelt werden. Eine Anzahl von Beispielen zeigen die Leistungsfähigkeit der Methode.

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Authors and Affiliations

  1. Milton S. Eisenhower Research Center, Applied Physics Laboratory, The Johns Hopkins University, 20707, Laurel, Maryland, USA

    D. W. Fox & J. R. Kuttler

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  1. D. W. Fox
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  2. J. R. Kuttler
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This work was supported by the Naval Sea Systems Command, U.S. Department of the Navy, under Contract N00024-81-C-5301.

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Fox, D.W., Kuttler, J.R. Sloshing frequencies. Z. angew. Math. Phys. 34, 668–696 (1983). https://doi.org/10.1007/BF00948809

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