A semi-analytical method is applied to investigate the propagation of flexural wave over multiple bottom-standing porous barriers with variable porosity beneath an ice cover under the assumption of linearised theory of water waves. Eigenfunction expansion method is used to express the velocity potential explicitly in terms of non-orthogonal eigenfunctions. Utilizing mode coupling relations satisfied by aforesaid eigenfunctions, the boundary value problem is reduced to a set of coupled Fredholm-type integral equations. These integral equations are solved by multi-term Galerkin’s method involving the Chebychev polynomials (multiplied by proper weights) as basis functions . The reflection and transmission coefficients, hydrodynamic forces and dissipated wave energy at the barriers are presented both analytically and graphically. A notable effect of the porosity of barriers and flexural rigidity of the ice cover on wave propagation is recorded. Bragg resonance of the flexural gravity waves due to the presence of four vertical porous barriers is observed and shown graphically. Efficiency of the present study is confirmed through a good agreement of the present results and the existing results available in the literature.

在水波线性化理论的假设下，采用半分析方法研究了弯曲波在冰层下多个底部可变孔隙度的底部多孔多孔屏障上的传播。本征函数展开法用于根据非正交本征函数来明确表示速度势。利用上述特征函数满足的模式耦合关系，将边值问题简化为一组耦合的Fredholm型积分方程。这些积分方程是通过将Chebychev多项式（乘以适当权重）作为基函数的多项Galerkin方法求解的。分析和图形显示了障碍物的反射和透射系数，流体动力和耗散的波能。记录了障碍物的孔隙率和冰盖的抗弯刚度对波浪传播的显着影响。观察到并以图形方式显示了由于存在四个垂直多孔屏障而引起的弯曲重力波的布拉格共振。本研究的有效性是通过对当前结果和文献中现有结果的良好共识来证实的。