应用比例边界有限元法研究波浪与带狭缝三箱作用的共振现象

Research on the hydrodynamic influence from the gaps between three identical boxes by a scaled boundary finite element method

比例边界有限元法(SBFEM)是一种半解析的新数值分析方法,比完全数值方法具有更高的分析精度。本文应用该方法求解波浪与有限水深中三个相同,但之间存在狭缝的二维固定方箱的作用问题,为波浪与多模块超大型浮体的相互作用提供一些规律。文中给出了各箱的波浪力及反射、透射系数的数值结果,与BEM结果进行了比较,吻合良好。发现波浪与三箱的作用存在双共振现象而且中间箱的共振形式与两边箱不同。进一步分析了箱体吃水深度、狭缝宽度和箱体宽度对三箱共振频率的影响。这对超大型浮体水动力分析和结构设计具有一定的参考价值。数值结果证实该方法用较少单元便能得到精确结果,这为超大型浮体的水动力分析提供了一个可行的分析方法。

The present study aims to give some general hints about hydrodynamic interactions for water wave action with a large floating structure composed of a number of box-shaped modules with small gaps between them. The problem of wave action with three identical 2D boxes in a fixed mean position in a finite water depth is computed by the sealed boundary finite element method and compared with a BEM. Sharp peak responses for both horizontal and vertical wave forces on each block are found around two closely special resonance frequencies. While horizontal wave force and vertical wave force on the middle box resonate only around one of the special resonance frequencies, which is different from the ones on both the up wave box and the leeside box. The resonance frequencies are influenced by box draft, box width and gap width. Examinations are carried out demonstrate the influence of the three variables on the resonance frequency. The present results are of practical significance to design of links of modules for very large floating structures. The result shows that the present method yields excellent result with less unknowns and quick convergence. It has a potential for analyzing very large floating structures and takes the gaps into consideration without numerical difficulties.