Characteristics of Bragg Reflection of Water Waves by Multiple Vertical Flexible Membranes

Bragg reflection of water waves by multiple vertical flexible membranes in water of uniform depth is investigated based on the assumption of linear wave theory and small membrane deflection. The multiple vertical flexible membranes consist of several floating vertical flexible membranes which are installed with both ends fixed. First, a single vertical flexible membrane in water waves is considered, and the reflection and transmission coefficients are obtained based on the eigenfunction expansion method and the least square method. Then the interaction of water waves with the multiple vertical flexible membranes is studied. Using the reflection and transmission coefficients obtained for the single flexible membrane, the reflection and transmission coefficients of the multiple vertical flexible membranes are obtained based on the wide spacing approximation. The proposed method is proved to be efficient by comparing the calculated coefficients with the results published in literature. The characteristics of Bragg reflection, such as the occurring condition, the primary amplitude and the effective bandwidth, are systematically investigated under various factors including the number, the tension, the draft and the spacing of membranes. The results of the present study have certain reference value for design of multiple vertical flexible membranes as effective floating breakwaters.