Prestressed vibrations of partially filled tanks containing a free-surface fluid: finite element and reduced order models

Abstract

In linear vibration analysis of partially filled elastic tanks [1], even if the the structure is submitted by a gaz or a liquid pressure, the reference configuration is generally used without the effect of static loads. In the case of very thin structures or soft material, the static state is considered as prestressed, due to geometrical nonlinearities of the deformed tank. The global stiffness of the structure may change in function of the fluid volume amount [2, 3, 4]. The aim of the paper is to quantify the prestressed effets on the linearized dynamic behavior of the fluid-structure system. The chosen methodology is the following: (i) A quasi-static solution is computed from an empty to a fully filled state of the tank, by considering geometrical nonlinearities and hydrostatic follower forces [5] (no volumetric mesh of the fluid is needed for this step); (ii) after a volumetric remeshing of the fluid at each states, a linearized hydroelastic displacement-pressure formulation around the prestressed state, without gravity effects, is established; (iii) a reduced basis of the hydroelastic problem is generated by using prestressed dry modes to minimize the computation of the added mass matrix. Numerical examples are given to illustrate the proposed approaches.