Acoustic approximation in the slamming problem

The plane unsteady problem of the deflection of a solid, slightly curved plate in collision with an ideal weakly compressible liquid is considered. In order to describe the impact process, the acoustic approximation and the method of normal modes are used. The analysis is focused on the supersonic stage of the impact when the liquid surface remains undisturbed outside the contact spot between the solid plate and the liquid. However, the positions of the contact points are unknown in advance, in contrast to the case of undeformable body impact, and have to be found together with the liquid flow, the pressure distribution, and the bottom deformations. It was shown that the duration of the supersonic stage depends on the entering body elasticity. A spray jet is formed earlier and the stage at which the liquid compressibility is a governing factor is shorter than under rigid-body impact. It is revealed that the elastic plate deflection is quite small and can be satisfactorily approximated by a few modes. On the other hand, the calculation of the bending stress distribution needs a much greater number of normal modes. The pressure distribution over the contact region is quite difficult to find by the mode method; an alternative approach is suggested.