Analytical Modeling of the Underwater Shock Response of Rigid and Elastic Plates Near a Solid Boundary

In this paper, analytical solutions are derived for the case when an elastic water-backed plate (WBP) is subject to an exponential shock loading near a fixed solid boundary. Two cases, a rigid plate and an elastic plate represented by two mass elements connected by a spring and a dashpot, are studied. The analytical solution is extended from Taylor's (1963, “The Pressure and Impulse of Submarine Explosion Waves on Plates,” Scientific Papers of Sir Geoffrey Ingram Taylor, Vol. 3, G. K. Batchelor, ed., Cambridge University Press, Cambridge, UK, pp. 287–303) floating air-backed plate (ABP) model and the water-backed plate model of Liu and Young (2008, “Transient Response of Submerged Plates Subject to Underwater Shock Loading: An Analytical Perspective,” J. Appl. Mech., 75(4), 044504; 2010, “Shock-Structure Interaction Considering Pressure Precursor,” Proceedings of the 28th Symposium on Naval Hydrodynamics, Pasadena, CA). The influences of five parameters are studied: (a) the distance of the fixed boundary from the back plate $d$⁠, (b) the fluid structure interaction (⁠$FSI$⁠) parameter $φ$ of the plate, (c) the stiffness of the plate as represented by the natural frequency of the system $T$⁠, (d) the material damping coefficient $CD$ of the plate, and (e) the pressure precursor (rise) time $θr$⁠. The results show that the pressure responses at the front and back surfaces of the plate are greatly affected by the proximity to the fixed boundary, the fluid-structure interaction parameter, the ratio of the shock decay time to the natural period of the structure, and the rise time of incident pressure. The effect of structural damping (assuming a typical material damping coefficient of 5%) is found to be practically negligible compared to the other four parameters.