Hydrodynamic response of dual obliquely submerged non-uniform flexible thin plates

Abstract

Examining inclined flexible plates with variable thickness becomes crucial when it comes to optimizing or achieving controlled reflection and transmission of waves, especially for the construction of breakwaters. Unlike horizontal breakwaters, inclined barriers have the ability to penetrate through numerous layers of the fluid, having different particle velocities and foster their interactions. This causes wave breaking which leads to loss of wave energy. Also, despite exhibiting a similar behavior, vertical structures do not attenuate waves as effectively as inclined ones do. Additionally, the resonant motion of the fluid trapped between two structures proves to enhance the attenuation, thus it is recommended to include dual structures in the model rather than just one. Therefore in the present study, we examine the water wave scattering phenomenon by a pair of symmetric flexible thin plates with non-uniform thickness obliquely submerged in deep water. We use the linear water wave theory and Kirchhoff’s thin plate theory to model the physical problem. The boundary value problem is converted into a system of coupled integral equations using repeated integration and Green’s integral theorem. Using appropriate approximations, this system is solved and its solutions are used to determine numerical values of different hydrodynamic quantities. Results of two horizontal as well as two vertical plates could be obtained from the present model, thus it is a very general model. Also results are illustrated to analyze the contribution of the thickness variation and the inclinations of the two flexible plates towards the wave scattering process and some related physical quantities.