Keywords: flow induced vibrations, cabin noise attenuation, viscoelastic supports, topology optimization.

In this work we consider the influence and optimization of the support properties of a panel on its vibrational response to external flow. Our purpose is to enhance the dissipation of energy in the panel, thereby reducing structure-borne noise. The attenuation of the flow or engine-induced structural vibration is a desirable feature in many applications, namely in aircraft structures.

Flow-induced structural vibrations is a well known topic and has been the subject of many previous works, [1,2]. In particular, several studies have been devoted to the characterization and attenuation of air cabin sound generation by fuselage panels, resulting from external flow excitation. Since the fuselage skin is usually riveted to stringers and very strong ring frames, each skin section may be simulated as an individual panel, [3]. The supports will be given by the stringers and/or ring frames attachments.

In this particular case study, we are given two materials, with different stiffness characteristics. These materials are used to fasten and seal the panel to the fuselage over a rectangular design domain. A high-fidelity model for a rectangular panel and its viscoelastic supports, which are simulated by a distribution of translational springs and dampers, was developed and validated with the literature, and is used to determine the optimal layout of the two materials that minimizes the induced vibrations, and consequently, the noise production. To this end, we follow a topology optimization approach. Specifically, we use the spectral level set methodology, which is a tool to formulate topology optimization problems.

We concluded that it is possible to decrease considerably the amount of high stiffness material with a negligible increase in induced noise. In particular, we obtained an optimal layout with 50% of high stiffness support material with an increase of 2 dB.

1

J. Park, L. Mongeau, T. Siegmund, "Analysis of the flow-induced vibrations of viscoelastically supported rectangular plates", Journal of Sound and Vibration, 261:225-245, 2003. doi:10.1016/S0022-460X(02)00955-0

2

A. Berry, J.-L. Guyader, J. Nicolas, "A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions", Journal of the Acoustical Society of America, 88:2782-2802, 1990. doi:10.1121/1.399682

3

B.L. Liu, L.P. Feng, A. Nilsson, "Sound transmission through curved aircraft panels with stringer and ring frame attachments", Journal of Sound and Vibration, 300:949-973, 2007. doi:10.1016/j.jsv.2006.09.008

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