Impulsive motion of floating bodies and generated loads

In the present paper asymptotic estimates of the impact loads generated after the sudden start of bodies originally floating on the free surface are derived. The analysis is focused on a stage during which compressible effects are already over whereas the gravity is still negligible. Within the assumptions of an ideal and incompressible fluid and of a potential flow, the solution is written in the form of an asymptotic expansion up to the second order. The non-dimensional displacement of the body plays the role of a small parameter. Owing to the singularity of the leading order solution at the initial contact point between body and free surface, the method of matched asymptotic expansions is used. An inner problem is formulated under a set of time-dependent stretched variables, solution of which is properly matched at the far field with the inner limit of the outer solution. It is shown that the eigensolution of the boundary value problem with boundary conditions of the mixed type plays an important role. In terms of hydrodynamic loads, the eigensolution term is responsible for a noninteger power of time which, being negative in some cases, can lead to unbounded impact loads just after the sudden start. The theory is developed for two-dimensional flared bodies, a two-dimensional flat plate and an axisymmetric disc. Comparisons among theoretical and numerical results are established exhibiting a fairly good agreement.