Complex resonances in the water-wave problem for a floating structure
Complex resonances in the water-wave problem for a floating structure
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DOI：
10.1017/s0022112005005021
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发表时间：
2005-07
影响因子：
3.7
通讯作者：
P. Mciver
中科院分区：
文献类型：
--
作者：
P. Mciver
这项工作涉及的线性理论的水波应用到运动的浮动结构，限制在某种程度上的运动的一部分的自由表面（这样的结构的一个例子是一个浮动圆环）。当这种类型的结构在入射的单色波中保持固定，或被迫以规定的速度进行时间谐波运动时，流体运动的振幅将在某些频率下具有局部最大值。当扩展到复频域时，这些共振对应于散射和辐射势的极点。它示出在这项工作中，在一般情况下，这些极点的位置在散射和辐射的潜力将不符合的极点出现在速度潜力的耦合问题时，结构是自由移动的位置。耦合问题的势的极点与运动方程的结构速度的解相关联。当物理量如流体运动的振幅作为（真实的）频率的函数被检查时，在从辐射和散射问题到耦合问题的过程中，通常将存在谐振频率的偏移。这种移动的幅度取决于结构的几何形状及其系泊方式。
This work is concerned with the linearized theory of water waves applied to the motion of a floating structure that restricts in some way the motion of a portion of the free surface (an example of such a structure is a floating torus). When a structure of this type is held fixed in incident monochromatic waves, or forced to move time harmonically with a prescribed velocity, the amplitude of the fluid motion will have local maxima at certain frequencies of the forcing. These resonances correspond to poles of the scattering and radiation potentials when extended to the complex frequency domain. It is shown in this work that, in general, the positions of these poles in the scattering and radiation potentials will not coincide with the positions of the poles that appear in the velocity potential for the coupled problem obtained when the structure is free to move. The poles of the potential for the coupled problem are associated with the solution for the structural velocities of the equation of motion. When physical quantities such as the amplitude of the fluid motion are examined as a function of (real) frequency, there will in general be a shift in the resonant frequencies in going from the radiation and scattering problems to the coupled problem. The magnitude of this shift depends on the geometry of the structure and how it is moored.