Modeling fluid-structure interactions during impact loading of water-backed panels

Understanding the response of water-backed panels to impact loading is of paramount importance in the design of marine and aerospace structures. In this theoretical study, we propose a modeling framework to investigate the two-dimensional, nonlinear hydroelastic response of thin structures. Within Euler-Bernoulli beam theory, we account for nonlinear stiffening due to membrane stretching. We demonstrate a closed-form solution for the fluid potential flow, which affords the exact computation of the hydrodynamic loading. The Galerkin discretization is used to cast the governing nonlinear integro-differential equation into a set of nonlinear ordinary differential equations. Two different semi-analytical solutions are established, by using the in-vacuum linear mode shapes of the beam and Hermitian finite element basis functions. Results are verified against full two-dimensional finite element simulations. We conduct a parametric study to elucidate the role of the beam thickness and the functional form of the impact loading. Our results indicate that the water-backing has a critical role on the structural dynamics, which is stronger for thin beams subject to rapid pulses. The model fills a significant gap in the technical literature, holding promise to inform the design of experimental setups and assist in the analysis of observations on water-backed panels.