Abstract
We consider small transient motions of a coupled system constituted by a linearly elastic body and two heavy incompressible non-Newtonian fluids. The fluids have free surfaces where surface tension effects are taken into account. We propose a mathematical modeling which involves a nonlinear evolution equation in Hilbert space of possible states with finite mechanical energy for the whole fluid-structure system. We obtain existence and uniqueness results, and study the influence of surface tension. Eventually we describe and justify a finite element method to compute numerical solution for small motions. If the structure is immersed in an unbounded sea, we introduce a sequence of larger and larger lakes with a condition of energy absorption by the edges.