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.

On considère le problème du ballottement dans un demi-espace couvert part un couvercle rigide avec des ouvertures. On étudie la dépendance de la valeur propre fondamentale par rapport à la forme de la région de surface libre, sous l'hypothèse que l'aire de cette région est fixée. Pour citer cet article : V. Kozlov, N. Kuznetsov, C. R. Mecanique 330 (2002) 723-728.