Abstract Complete analytical solution for the normally incident water wave scattering by a porous flexible vertical elastic plate or tensioned membrane is found. The physical problem in a half-plane is reduced to a couple of equivalent quarter-plane problems by allowing incident waves from either direction of the structure. In the same way, quarter-plane boundary value problems are posed for solid wave potentials that are solutions of the scattering problem involving a rigid structure of the same geometric configuration. Then, two novel integral relations are introduced to establish a link between the required solution wave potentials and few resolvable solid wave potentials. Explicit expressions for the scattering quantities such as the reflection and the transmission coefficients are obtained. Also, the deflection of the flexible vertical structure and the solution potentials are determined analytically. Numerical results for the explicitly derived scattering quantities and structure deflections are presented.

中文翻译：

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涉及垂直柔性多孔结构的散射问题的显式解

摘要 找到了多孔柔性垂直弹性板或张拉膜对垂直入射水波散射的完整解析解。通过允许来自结构任一方向的入射波，半平面中的物理问题被简化为几个等效的四分之一平面问题。以同样的方式，对于固体波势提出了四分之一平面边界值问题，这些势是涉及相同几何构型的刚性结构的散射问题的解。然后，引入了两个新的积分关系，以在所需的解波势和少数可分辨的固体波势之间建立联系。获得了散射量（例如反射和透射系数）的显式表达式。还，柔性垂直结构的挠度和溶液电位是通过分析确定的。给出了明确导出的散射量和结构偏转的数值结果。