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.