Within the framework of linearised theory of water waves, a model of oblique wave scattering by obstacles in the form of thin multiple surface-piercing porous barriers having non-uniform porosity is analysed. Herein, we consider a flexible base in an ocean of uniform finite depth. The flexible base surface is modelled as a thin elastic plate under the acceptance of Euler–Bernoulli beam equation. With the aid of eigenfunction expansion method along with mode-coupling relations, four Fredholm-type integral equations are obtained from the boundary value problem. The multi-term Galerkin approximations in terms of Chebychev polynomials multiplied by suitable weight functions are used for solving those integral equations. Analytic solutions for different hydrodynamic quantities (viz. reflection coefficients, transmission coefficients, dissipated wave energy and non-dimensional wave force) are determined, and those quantities are displayed graphically for various values of the dimensionless parameters. It is observed from the graphical representations that the permeability of the barriers and thickness of the bottom surface play a crucial role in modelling of efficient breakwaters.

在水波线性化理论的框架内，分析了斜波由障碍物散射的模型，这些障碍物是具有不均匀孔隙率的薄薄的多个穿透表面的多孔障碍物的形式。在这里，我们考虑在均匀有限深度的海洋中的柔性基础。在接受Euler–Bernoulli梁方程的情况下，可弯曲的基础表面被建模为薄的弹性板。借助特征函数展开法和模耦合关系，从边值问题得到了四个Fredholm型积分方程。用Chebychev多项式乘以合适的权函数得出的多项Galerkin近似值用于求解这些积分方程。不同流体动力量的解析解（即反射系数，透射系数，确定消散波能量和无量纲波力，并以图形方式显示这些量以表示无量纲参数的各种值。从图形表示中可以看出，屏障的渗透性和底部表面的厚度在有效防波堤的建模中起着至关重要的作用。