Reduced models for modal analysis of fluid–structure systems taking into account compressibility and gravity effects

It is proposed to investigate and discuss, from theoretical point of view, various reduced order variational formulations for modal analysis of linear vibrations of bounded fluid–structure systems with free surface, taking into account possible gravity/compressibility interactions, in a non-homogeneous fluid situation.Those formulations are based on substructural synthesis techniques and various modal reduction schemes are then obtained.In a previous paper, various original formulations have been exhibited associated to numerical validation. The present paper starts from those formulations in order to construct theoretically various reduced order models.