Treatment of hydroelastic impact of flexible wedges

Understanding the role of structural flexibility on the response of lightweight structures to water impact is pivotal for the design of marine vessels and aircraft. While several modeling schemes have been proposed to study hydroelastic slamming of flexible wedges, most of these studies focus on water entry at a constant speed and assume simply supported boundary conditions for the plates forming the wedge. Here, we propose a novel modeling framework for the analysis of two-dimensional hydroelastic slamming of flexible wedges entering the water surface in free fall with arbitrary boundary conditions. Euler-Bernoulli beam theory is used to model the wedge kinematics and Wagner theory is adopted to study the flow physics. A mixed boundary value method is utilized to compute the velocity potential as a function of the structural deformation. A Galerkin formulation is derived by projecting the governing equations on a polynomial set of basis functions, which is constructed using the Gram-Schmidt algorithm. The selection of such a polynomial expansion leads to the closed-form computation of all the salient integrals associated with the hydrodynamic loading. A Newmark-type integration scheme is finally used to solve the coupled equations in time. Results are validated through comparison with available semi-analytical, computational, and experimental findings across a wide range of hydroelasticity factors and boundary conditions. The model can be used to gather important insight on the role of structural flexibility on the hydrodynamic loading experienced by the wedge, along with the resulting keel entry depth and structural deformation.