We compute the natural frequencies for the oscillations of the free boundary of gravity waves in contact with a solid container. First, we study the case of a semicircular shaped container. We deduce an integrodifferential evolutionary equation for the linearized free boundary and impose pinned-end and free-end boundary conditions. For both cases, the natural oscillations frequencies for the free surfaces are provided and compared with the frequencies in the absence of solid walls. Then, we study the effect of having an underwater rectangle-shaped bottom in a rectangular container and the corresponding frequencies. The method introduced can be applied to arbitrary 2D containers, with all the information on their geometry contained into a matrix (related to the conformal mapping into a half-plane) that appears as a factor in a linear system for the computation of eigenfrequencies.

我们计算与固体容器接触的重力波自由边界振荡的固有频率。首先，我们研究一个半圆形容器的情况。我们推导了线性自由边界的积分微分演化方程，并施加了固定端和自由端边界条件。对于这两种情况，都提供了自由表面的固有振动频率，并将其与没有实心壁的频率进行了比较。然后，我们研究在矩形容器中放置水下矩形底部的效果以及相应的频率。所介绍的方法可以应用于任意2D容器，