On the fundamental sloshing frequency in the ice-fishing problemSur la fréquence de ballottement principale dans le problème de la glace avec trous pour pêcher |
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Authors: | Vladimir Kozlov Nikolay Kuznetsov |
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Affiliation: | 1. Department of Mathematics, Linköping University, 58183 Linköping, Sweden;2. Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol''shoy pr. 61, St. Petersburg 199178, Russia |
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Abstract: | The sloshing problem is considered in a half-space covered by a rigid dock with apertures. The dependence of the fundamental sloshing frequency on the shape of the free surface region is studied. It is proved that the inequality holds between the fundamental eigenvalues corresponding to two different regions if some conditions are fulfilled. These conditions are verified for particular classes of regions of a fixed area in order to demonstrate that the disk yields the maximum of the fundamental eigenvalue for each of these classes. On the other hand, examples of regions are constructed for which the fundamental eigenfrequency is larger than that for the circular aperture of the same area and even as large as one wishes. To cite this article: V. Kozlov, N. Kuznetsov, C. R. Mecanique 330 (2002) 723–728. |
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Keywords: | fluid mechanics sloshing problem fundamental eigenvalue integral operator variational principle mécanique des fluides oscillations libres d'une fluide valeur propre fondamenale opérateur intégral principe variationnelle |
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