标题： 二维水波在自由浮动物体存在下的情况：无俘获模态的条件 显示英文标题

标题： Two-dimensional water waves in the presence of a freely floating body: conditions for the absence of trapped modes

摘要： 对由水和一个在其中自由漂浮的物体组成的机械系统，研究了耦合运动。 水占据半空间或恒定深度的层，其中浸入一个无限长的表面穿透圆柱体，从而允许我们研究二维模式。 假设运动在平衡附近为小振幅，适用线性设置，并且对于时间谐波振动，它简化为一个以振动频率作为谱参数的谱问题。 重要的是，该问题的一个关系相对于参数是线性的，而另外两个关系则相对于它为二次的。 在此框架下，证明了水运动的总能量是有限的，整个系统的能量均分成立。 在此基础上，证明了当其频率超过依赖于圆柱体特性的界限时，无法捕获波模式，而其几何结构受到一些限制，并且在某些情况下，对模式类型施加了某些限制。 显示英文摘要

摘要： The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes. Under the assumption that the motion is of small amplitude near equilibrium, a linear setting is applicable and for the time-harmonic oscillations it reduces to a spectral problem with the frequency of oscillations as the spectral parameter. It is essential that one of the problem's relations is linear with respect to the parameter, whereas two others are quadratic with respect to it. Within this framework, it is shown that the total energy of the water motion is finite and the equipartition of energy holds for the whole system. On this basis, it is proved that no wave modes can be trapped provided their frequencies exceed a bound depending on cylinder's properties, whereas its geometry is subject to some restrictions and, in some cases, certain restrictions are imposed on the type of mode.