Abstract The study deals with the scattering of obliquely incident gravity waves by a horizontal floating flexible porous plate in the water of finite depth having a variable bottom bed. The problem when a vertical rigid wall is placed in the downstream of the plate is also considered. The problem is analyzed under the assumptions of small amplitude water wave theory and structural responses. The undulated bottom bed is finitely extended and lies beneath the floating plate regions. A coupled eigenfunction expansion - boundary element method is used for the solution purpose. Energy balance relations for wave scattering in the presence of the flexible plate and when the vertical rigid wall is placed in the downstream are derived and used to check the accuracy of the numerical results. The effect of sinusoidally varying bottom topography, plate porosity and heading angle of the incident wave on the Bragg resonance is analyzed. Moreover, various results are computed and analyzed to study the role of the wave parameters, bottom undulation and floating porous flexible plate on wave scattering. The proposed solution methodology can be easily extended to deal with wave-structure interaction problems of varied structural configurations and bottom bed.

中文翻译：

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浮动柔性多孔板在可变测深区域上的水波散射

摘要 研究了水平浮动柔性多孔板在具有可变底床的有限深度水中对倾斜入射重力波的散射。还考虑了在板的下游放置垂直刚性壁时的问题。该问题在小振幅水波理论和结构响应的假设下进行分析。起伏的底床有限地延伸并位于浮板区域下方。耦合本征函数展开 - 边界元方法用于求解目的。推导了柔性板存在和垂直刚性壁放置在下游时波浪散射的能量平衡关系，并用于检查数值结果的准确性。正弦变化的底部地形的影响，分析了布拉格共振上入射波的板孔隙率和航向角。此外，计算和分析了各种结果，以研究波浪参数、底部起伏和浮动多孔柔性板对波浪散射的作用。所提出的求解方法可以很容易地扩展到处理不同结构配置和底床的波浪-结构相互作用问题。