Compressibility and gravity effects in internal fluid–structure vibrations: Basic equations and appropriate variational formulations

Various variational formulations for the linear vibrations of bounded fluid–structure systems, taking into account possible gravity/acoustic interactions are investigated and discussed. The system consists of a tank partially filled with an inviscid liquid. Two situations corresponding to the cases of a homogeneous and a non-homogeneous liquid are considered. In this respect, the basic equations describing the interactions between acoustic and gravity waves are derived and appropriate variational formulations are constructed.