Propagation of Hydrodynamic Wave Past Two Vertically Submerged Flexible Barriers of Non-Uniform Thickness

Abstract

Abstract In the literature related to linear water waves, most of the works have considered thin structures to have constant or uniform thickness. This assumption is based on the fact that the thickness variations in structures that are thin have no significant impact on the hydrodynamic quantities. But in the present work, we have shown that it is not so; even for thin structures, thickness variations can cause major changes in the physical quantities like plate deflection and the hydrodynamic force experienced by the structure. Also, in general, for an intensive study of the fluid-structure interaction problems, it is necessary to include the structural variations in the models for a better understanding of the phenomena. The transition from one barrier to a pair of barriers might be interesting because they enclose a water column which leads to near-resonant motion. This feature might be helpful to engineers for the purpose of construction of breakwaters. Thus in the present paper, we assess the hydrodynamic response of a pair of completely submerged vertical flexible barriers of non-uniform thickness to incoming surface gravity waves using hypersingular integral equations. The fluid domain is considered to be of infinite depth, and further, both the barriers are assumed to have clamped-free ends. By considering Kirchhoff’s thin plate theory, the described problem is reduced into a boundary value problem, which is solved by converting it into a system of coupled Fredholm integral equations using the classical method of integration and Green’s integral theorem. Further, the obtained integral equations system is converted to a matrix system of linear equations using appropriate approximations for the unknown quantities to obtain numerical solutions. With the help of MATLAB software the matrix system is solved, whose solutions are then used to determine numerical estimates of various physical quantities. The method used and the numerical results are validated by comparing them in the limiting cases of dual flexible barriers of constant thickness which are already available in the literature. Some selective graphical results are depicted in order to show the effect of the non-uniform thickness of the two flexible barriers on their hydrodynamic response by choosing certain thickness profiles.