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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 106

An Energy Model for Mid-High Frequency Elasto-Acoustic Problems Using the Finite Element Method

M. de Rochambeau1, M. Ichchou1, L. Jezequel1 and B. Troclet2

1Laboratory of Tribology and Systems Dynamics, UMR CNRS 5513, Ecole Centrale de Lyon, LTDS, Ecully, France
2Missile Structural Analysis Department, EADS Astrium ST, Les Mureaux, France

Full Bibliographic Reference for this paper
M. de Rochambeau, M. Ichchou, L. Jezequel, B. Troclet, "An Energy Model for Mid-High Frequency Elasto-Acoustic Problems Using the Finite Element Method", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 106, 2008. doi:10.4203/ccp.89.106
Keywords: fluid-structure interaction, elasto-acoustic system, optimization, modal analysis, SEA-like method, SEA.

The study of fluid-structure interaction in the mid-frequency domain is necessary to model aeronautical and spatial structures. Indeed those structures may be excited by random and broadband excitations during the atmospheric flight, which can generate noise and vibrations in the structure and deteriorate equipment.

In the mid-frequency domain, the fluid-structure interaction cannot be performed using a finite element (FE) method or statistical energetic analysis (SEA): the modal overlap is too high to use a FE model efficiently and too low to use an SEA model accurately. Therefore a hybrid FE/SEA method is introduced to model fluid-structure interactions: the SEA-like method.

The SEA-like method is an energy distribution method and is applied on a structure through an SEA-like matrix. The calculation of the SEA-like matrix on any system was mainly studied by Mace [1,2]. He calculated the SEA-like coefficient using the modes of the whole system. Using the property of orthogonally of the modes, he obtained an expression for the SEA-like coefficients.

Pan [4,5] studied the mid-frequency fluid-structure coupling on a coupled panel-cavity system. He applied a modal analysis to the system using the modes of the uncoupled systems. He further compared the frequency and spatial coupling between the cavity modes and the panel modes in order to determine the predominant pairs of modes.

In order to study the fluid-structure interaction using an SEA-like method, the coupled panel-cavity system studied by Pan [5] is modelled. A sub-structure method is used and the SEA-like coefficients are calculated. The calculation is then validated using an SEA model of the panel-cavity system. This SEA model can be calculated using Maidanik's theory [3] of the radiation of finite panels. An energy distribution matrix is then calculated using the SEA modelling. The SEA-like model is validated by the comparison of this last matrix with the SEA-like matrix.

The study of the coupling between the panel and cavity modes on the modelling based on Pan's calculations leads to the simplification of the modelling of the fluid-structure interaction. Applying the results of the SEA-like modelling using the FE method and Mace's formulations, the SEA-like method can be extended to industrial applications of fluid-structure interactions.

Mace B.R., "Statistical energy analysis, energy distribution models and system modes", Journal of Sound and Vibration, 264, 391-409, 2003. doi:10.1016/S0022-460X(02)01201-4
Mace B.R., "Statistical energy analysis: coupling loss factor, indirect coupling and system modes", Journal of Sound and Vibration, 279, 141-170, 2005. doi:10.1016/j.jsv.2003.10.040
Maidanik G., "Response of Ribbed Panels to the Reverberant Acoustic Fields", Journal of the Acoustical Society of America, 34(2), 809-826, 1962. doi:10.1121/1.1918200
Sum K.S., Pan, J., "An analytical model for bandlimited response of acoustical-structural coupled systems. I. Direct sound field excitation", Journal of the Acoustical Society of America, 103(2), 911-923, 1998. doi:10.1121/1.421208
Sum K.S., Pan, J., "A study of the medium frequency response of sound field in a panel-cavity system", Journal of the Acoustical Society of America, 103(3), 1510-1519, 1998. doi:10.1121/1.421288

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