Dynamic Analysis of a Coupled Fluid Structure Problem With Fluid Sloshing

The present paper is related to the study of a generic linear coupled fluid/structure problem, in which an elastic beam is coupled with an inviscid fluid, with or without sloshing effects. A previous study [18] focussed on added mass effects; the present study is devoted to the coupling effects between fluid sloshing modes and structure with fluid added mass modes. The discretization of the coupled linear equations is performed with an axisymmetric fluid pressure formulated element, expanded in terms of a FOURIER series [14]. Various linear fluid model are taken into account (compressible, uncompressible, with or without sloshing) with the corresponding coupling matrix operator. The modal analysis is performed with a MATLAB program, using the non-symmetric LANCZOS algorithm [16]. The temporal analysis is performed with classical numerical techniques [10], in order to describe the dynamic response of the coupled problem subjected to a simple sine wave shock. The coupling effects are studied in various conditions represented by several non-dimensionnal numbers [12] such as the dynamic FROUDE number and the mass number, based on the geometrical and physical characteristics of the coupled problem. Comparisons are performed on the coupled problem with or without free surface modeling, with a model and temporal analysis. Coupling effects are exhibited and quantified; the numerical results obtained in the modal analysis here are in good agreement with other previous studies, carried out on different geometry [3,15]. The temporal analysis gives another point of view on the importance of the coupling effects and their importance at low dynamic FROUDE numbers. The present study gives and will be completed with a non-linear analysis (for both fluid and structure problems) of the coupled problem, using a finite element and finite volume explicit coupling procedure [19].