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Research Papers

Design Optimization With an Uncertain Vibroacoustic Model

[+] Author and Article Information
E. Capiez-Lernout1

Laboratoire de Mecanique (LaM), EA 2545, Universite Paris-Est, 5 Boulevard Descartes, 77454 Marne la Vallee, Cedex 02, Franceevangeline.capiezlernout@univ-paris-est.fr

C. Soize

Laboratoire de Mecanique (LaM), EA 2545, Universite Paris-Est, 5 Boulevard Descartes, 77454 Marne la Vallee, Cedex 02, Francechristian.soize@univ-paris-est.fr

1

Corresponding author.

J. Vib. Acoust 130(2), 021001 (Jan 30, 2008) (8 pages) doi:10.1115/1.2827988 History: Received July 07, 2006; Revised July 31, 2007; Published January 30, 2008

This paper deals with the design optimization problem of a structural-acoustic system in the presence of uncertainties. The uncertain vibroacoustic numerical model is constructed by using a recent nonparametric probabilistic model, which takes into account model uncertainties and data uncertainties. The formulation of the design optimization problem includes the effect of uncertainties and consists in minimizing a cost function with respect to an admissible set of design parameters. The numerical application consists in designing an uncertain master structure in order to minimize the acoustic pressure in a coupled internal cavity, which is assumed to be deterministic and excited by an acoustic source. The results of the design optimization problem, solved with and without the uncertain numerical model, show significant differences.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Structural-acoustic system

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Figure 2

Mean model of the master structure: plates (filled domain); frame (thick black line) (left) and mean finite element model of the structural-acoustic system (right)

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Figure 3

Convergence analysis: graph of function nr↦Conv(nr,51,100) for the structural-acoustic system with r0=0.005m and δKS=0.25

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Figure 4

Convergence analysis: graph of function NS↦Conv(500,NF,NS) for the structural-acoustic system with r0=0.005m and δKS=0.25 and for NF=11 (black line), NF=41 (dark gray line), and NF=51 (light gray line)

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Figure 5

Observation of the initial structural-acoustic system. Graph of function ν↦10log10(w̱0(2πν)) (thin black line). Confidence region (gray region) of the random observation W0(2πν) obtained with a probability level Pc=0.98. The horizontal axis is the frequency ν in hertz.

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Figure 6

Comparison between the design optimization and the robust design optimization. Graph of functions r↦10log10(wB1,∞+(r)) (black line) and r↦10log10(w̱B1,∞(r)) (gray line). The horizontal axis is the design parameter r.

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Figure 7

Graphs of function ν↦10log10(w̱D(2πν)) (thin black line) and of the confidence region (gray region) of the random observation 10log10(WD(2πν)) corresponding to the design optimization. The horizontal axis is the frequency ν in hertz.

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Figure 8

Graphs of function ν↦10log10(w̱RD(2πν)) (thin black line) and of the confidence region (gray region) of the random observation 10log10(WRD(2πν)) corresponding to the robust design optimization. The horizontal axis is the frequency ν in hertz.

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Figure 9

Comparison between the design optimization and the robust design optimization. Graph of functions r↦10log10(wB,∞+(r)) (black line) and r↦10log10(w̱B,∞(r)) (gray line). The horizontal axis is the design parameter r.

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Figure 10

Graphs of function ν↦10log10(w̱D(2πν)) (thin black line) and of the confidence region (gray region) of the random observation 10log10(WD(2πν)) corresponding to the design optimization. The horizontal axis is the frequency ν in hertz.

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Figure 11

Graphs of function ν↦10log10(w̱RD(2πν)) (thin black line) and of the confidence region (gray region) of the random observation 10log10(WRD(2πν)) corresponding to the robust design optimization. The horizontal axis is the frequency ν in hertz.

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