Three-dimensional impact onto a circular floating viscoelastic plate

A three-dimensional problem of vertical impact by a rigid smooth body onto a floating viscoelastic plate is considered within the framework of linear hydroelasticity. The liquid is assumed to be incompressible, inviscid, and of infinite depth. The plate is thin, of constant thickness, with free–free edge. The problem is coupled and unsteady. The upper surface of the plate is covered with a thin layer of soft material of constant thickness and negligible inertia. The impact occurs through this layer. The reaction force of the layer is described by a nonlinear one-dimensional Winkler–Kelvin–Voigt model. The soft layer prevents direct contact between the rigid body and the floating plate. A solution procedure applicable to plates of arbitrary smooth shape is described. It is based on the normal modes of the dry plate and the corresponding added-mass matrices. The coupled problem is reduced to a system of nonlinear ordinary differential equations governing the modal amplitudes, which is integrated in time using a fourth-order Runge-Kutta method. Impact loads acting on the floating plate are obrained as part of the solution. Numerical results are presented for a circular plate, for which the normal modes and the elements of the added-mass matrix are available in analytical form. It is shown that a large number of modes is required in three-dimensional hydroelastic slamming problems to achieve convergence of the solution. To reduce the computational cost, three approximate impact models are introduced. The hydrodynamic pressure at the plate–liquid interface, the three-dimensional plate deflections, and the strains within the plate are investigated for selected problem parameters. The obtained results are suggested for use in validating coupled three-dimensional computational algorithms for hydroelastic slamming.