Hydroelastic analysis of a simple oscillator impacting the free surface

The coupling between the hydrodynamic and elastic forces arising when a sim ple oscillator impacts the free surface is considered. The system is a two- mass oscillator, the lower mass being wedge-shaped, free falling on the fre e surface. Attention is devoted to a parametric investigation of the maximu m of both hydrodynamic and elastic forces induced by the impact. The study is performed by a simplified theoretical model and by a numerical simulatio n of the fluid-structure interaction. The theoretical model suggested here provides an efficient tool for the computation of the hydrodynamic and elas tic forces and of the corresponding maxima as a function of some parameters such as deadrise angle of the wedge, entry velocity, spring stiffness, and the masses, In particular, a closed-form expression for the critical value of the spring constant leading to the maximum elastic response is achieved as a function of the other parameters. Numerically, a panel method is adop ted to solve the boundary integral formulation for the velocity potential. A suitable model is introduced to deal with the flow singularity at the int ersection point between the free surface and the body contour. Time histori es of the hydrodynamic and elastic forces are computed for different values of the spring stiffness and are compared with the corresponding results pr ovided by the simplified theoretical model. The comparison shows that, desp ite the strong assumptions, the theoretical model allows a good estimate of the system critical condition.