Various modelling levels to represent internal liquid behaviour in the vibration analysis of complex structures

In the framework of the vibrational analysis of structures, we propose to focus here on methods available to take into account internal liquids (propellants for instance) in structure modelling. The case of a structure partially filled with incompressible liquids is very common and many industrial domains are interested in this issue especially in the transport and aerospace industries (wing tanks of aircrafts, liquid propelled launchers, etc.). Because the computing cost of a full time-solution of the Arbitrary Lagrange Euler equations of the problem becomes quickly prohibitive, a modal approach is generally preferred. This is the reason why the interest for linearized formulations of this fluid–structure interaction problem has never decreased since the first works initiated on this topic in the 1950s. The aim of this article is to give a review of different linear models that can be used to take into account an internal incompressible liquid in the vibratory analysis of a complex structure. Modellings of different complexity levels will be considered: from the simplest, which represents the liquid as a “frozen” mass, to a more recent model, which gives a linearized representation of the fluid sloshing and takes into account hydrostatic prestress effects, without forgetting the classical “hydroelastic added-mass” model. We will compare the results obtained with those modellings on an application example to exhibit their limitations and their domain of validation, and to illustrate the usefulness of the most sophisticated models in certain cases.