Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model

Abstract

International audienceThis paper deals with the development of the linear vibration of a general viscoelastic structure, with a local wall acoustic impedance, containing an inviscid compressible liquid (but with an additional volume dissipative term), with surface tension (capillarity) and sloshing effects, and neglecting the effects of internal gravity waves and the elas-togravity operator. The sloshing problems of incompressible liquids with capillarity effects in elastic structures exhibit a major difficulty induced by the boundary contact conditions on the triple line because the capillarity forces are forces per unit length while the elastic forces are forces per unit surface. The proposed framework has the following novel features: (i) introducing a new appropriate boundary condition for the contact angle condition compatible with a deformable structure considered here as viscoelastic, (ii) considering a compressible liquid while incompressibility hypothesis is generally used for FSI problems including capillarity phenomena, and (iii) constructing a reduced-order model for the computational coupled problem

Nonlinear Dynamical Analysis for Coupled Fluid-Structure Systems

“…is the nonlinear term issued from the large displacements/deformations induced by the geometrical nonlinearities. An adapted numerical nonlinear reduced-order model of order N requiring the numerical computation of the elastic modes of the structure with fluid added mass effect, of the acoustic modes of the fluid, and of the sloshing modes of the free surface [1] is proposed in [3]. Such computation on mid-power computers can be very challenging when large finite element meshes are involved.…”

“…The structural-acoustic system under consideration is made up of a tank structure filled with a linear inviscid compressible fluid. Gravity effects and surface-tension effects of the free surface and corresponding coupling terms are taken into account as described in [1]. A linear elastic constitutive equation is considered for the structure.…”

Solving generalized eigenvalue problems for large scale fluid-structure computational models with mid-power computers

“…This ROM is not constructed using a global ROB associated with the full coupled problem, but is constructed using the elastic modes of the structure with the added-mass effects, the acoustic modes of the liquid, and the sloshing/capillarity modes. The interest of such a formulation (see [27,28,29]) is to be able to select the modes that contribute to the responses in the frequency band of analysis and also to be able to implement the nonparametric probabilistic approach of model uncertainties in each part of the coupled system for which the level of uncertainties differs from a part to another one. It should be noted that this formulation differs from the vibroacoustics problems (without sloshing and surface tension effects) for which a ROM is constructed using a global ROB (see for instance [30]).…”

“…In the particular context of this fluid-structure interaction problem for which sloshing and surface tension effects are taken into account, many research have been performed (see for instance, [27,31,32,33]). In this paper, the formulation used is the one presented in [28,29] for which the adapted reduced-order model (ROM) has been evoked and is more detailed hereinafter. The construction of the ROM requires a modal characterization of the different parts of the fluid-structure system.…”

Modal Analysis of Liquid–Structure Interaction

“…is very common and many industrial domains are interested in this issue especially in the transport and aerospace industries (for instance liquid propelled launchers and satellites). Computational aspects of fluid-structure interaction and sloshing (with or without surface tension effects) may be found in [1,4,5,6,7,9,13,14,15,21]. We are here interested in the linear vibrational response of elastic structures partially filled with a liquid.…”