Using an advanced nonlinear fluid-structure reduced-order computational model, this work revisits and explains a resonance of the free surface of water contained in a thin elastic cylindrical tank, which was experimentally exhibited by Lindholm, 1962 and Abramson, 1966. The proposed simulation model allows the experimental setup to be reproduced. The structure undergoes large displacements and large deformations (geometrical nonlinear effects of the structure) that play an important role on the liquid vibrations. The experimental setup is simulated using a large-scale numerical model of the elastic cylindrical tank partially filled with water that is considered as a compressible fluid and that takes into account surface tension and sloshing effects. The results show that for a frequency external excitation in the frequency band [500, 2,500] Hz of the fluid-structure system, unexpected high-amplitude sloshing vibrations are observed in the frequency band [0, 150] Hz. The observed phenomenon, which cannot be reproduced with a linear fluid-structure model, is explained by the transfer of the vibrational energy from the frequency band of excitation into a low-frequency band (and then exciting the first sloshing modes) by a non-direct coupling mechanism between the structural modes and the sloshing modes.
This article proposes a method for solving generalized eigenvalue problems on medium-power computers with a moderate memory in the particular context of studying fluid-structure systems with sloshing and capillarity. This research was performed following many RAM problems encountered when computing the modal characterization of the system studied. The methodology proposed is one solution to reduce RAM and time required for the computation, by using methods such as double projection or subspace iterations.
In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid-structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid-structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.
This paper is devoted to the linear dynamics of liquid-structure interactions for an elastic structure filled with compressible liquid (acoustic liquid), with sloshing and with capillarity effects on the free surface in presence of a gravity field. The objective is to detail the formulation and to quantify the role played by the elasticity in the neighborhood of the triple contact line between the free surface of the compressible liquid and the elastic structure in presence of sloshing and capillarity effects. Most of the works consider that the structure is totally not deformable (rigid tank). Nevertheless, for taking into account the elasticity of the tank, some works have introduced an approximation, which consists in considering a locally undeformable structure in the neighborhood of the triple contact line. The theory presented requires the use of quadratic finite elements for discretizing a new introduced boundary condition. An application has specifically been constructed and presented for quantifying the role played by the elasticity of the structure in the neighborhood of the triple contact line.
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