The study of a interaction fluid-structure problem requires the calculation of fluid forces acting on moving boundaries. Since the first studies carried out by Stokes, a lot of work has been performed to derive various expressions of fluid forces, in particular for the case of simple geometry, such as infinite planes, spheres or circular cylinders. These bodies are subjected to elementary motions, namely harmonic motions or Dirac acceleration motions, (i.e. constant speed velocity motions). The present paper exposes a review of fluid forces exerted on accelerated rigid body in an incompressible viscous fluid initially at rest. The principal objective of this paper is to carry out a synthesis of the current literature and to develop a general analytical formulation of the fluid forces in order to deal with more general rigid body motions. The analytical formulation is exposed in the present paper for fluid forces acting on any moving body. This approach is limited to low displacements of the solid body, i.e. the non linear convective term of NS equation is not taken into account. The non-dimensional numbers is pointed out and detailed. The different solutions given in the literature are especially discussed with the influence of the viscosity compared to the irrotational model.

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