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Research Papers

SEA Coupling Loss Factors of Complex Vibro-Acoustic Systems

[+] Author and Article Information
N. Totaro1

Laboratoire Vibrations Acoustique, INSA-Lyon, Bâtiment St. Exupéry, 20, Avenue Albert Einstein, F69621 Villeurbanne Cedex, Francenicolas.totaro@insa-lyon.fr

C. Dodard, J. L. Guyader

Laboratoire Vibrations Acoustique, INSA-Lyon, Bâtiment St. Exupéry, 20, Avenue Albert Einstein, F69621 Villeurbanne Cedex, France

1

Corresponding author.

J. Vib. Acoust 131(4), 041009 (Jun 08, 2009) (8 pages) doi:10.1115/1.3086929 History: Received October 02, 2007; Revised June 06, 2008; Published June 08, 2009

Reliability of statistical energy analysis (SEA) models depends on good estimates of coupling loss factors (CLFs), modal densities, and damping loss factors. Statistical modal energy distribution analysis (SmEdA), a finite element based method to compute CLFs from uncoupled finite elements models of subsystems, is used to generate SEA CLF for general subsystems. This method is based on the basic SEA relations for coupled oscillators and on a dual modal formulation to describe the vibration of coupled subsystems. Previous works have demonstrated the use of the SmEdA method for structure-to-structure couplings. The current work extends the SmEdA process to structure-to-cavity couplings. The estimation of CLF using the SmEdA approach is compared, for a simple test case, to analytical results and a classical expression obtained with a wave approach. Results show good comparison with analytical results even below critical frequency, where the wave approach underestimates CLF. Finally, an industrial application has been carried out to demonstrate that the SmEdA approach can be used in the case of complex structures.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Power balance between two SEA subsystems

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Figure 2

Simply supported plate radiates into a cavity with rigid wall

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Figure 3

Principle of SmEdA method

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Figure 4

Coupling loss factors plate 1/cavity 1 (plate and cavity characteristics in Tables  21). ○: analytical approach, +: SmEdA approach, and ◻: wave approach.

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Figure 5

Coupling loss factors cavity 1/plate 1 (plate and cavity characteristics in Tables  21). ○: analytical approach, +: SmEdA approach, and ◻: wave approach.

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Figure 6

Coupling loss factors plate 1/cavity 2 (plate and cavity characteristics in Tables  21). –○–: analytical approach, – –○– –: analytical approach with resonant modes only, and –+–: SmEdA approach.

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Figure 7

Coupling loss factors plate 1/cavity 3 (–, Lz=0.2 m), plate 1/cavity 1 (– – –,Lz=0.7 m), and plate 1/cavity 4 (…, Lz=1 m) (plate and cavity characteristics in Tables  21). ○: analytical approach, +: SmEdA approach, and ◻: wave approach.

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Figure 8

Coupling loss factors. (a) plate 2/cavity 1 (h=1 mm), (b) plate 3/cavity 1 (h=2 mm), and (c) plate 1/cavity 1 (h=4 mm) (plate and cavity characteristics in Tables  21). ○: analytical approach, +: SmEdA approach, and ◻: wave approach.

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Figure 9

FEM meshes of validation case. Green: mesh of the cavity, blue: mesh of plate, and red: coupling surface.

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Figure 10

Comparison between analytical and numerical (FEM) results. (a) Coupling loss factor plate 1/cavity 1 and (b) coupling loss factor cavity 1/plate 1. –○–: SmEdA with analytic mode shapes and –+–: SmEdA with numerical (FEM) mode shapes.

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Figure 11

Meshes of the industrial application. The car cabin in composed of solid elements, the windshield is composed of shell elements, and the firewall is composed of shell elements.

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Figure 12

Coupling loss factors between firewall or windshield and the car cabin as a function of frequency. (a): CLF between structure and cavity and (b): CLF between cavity and structure. –+–: structure=windshield and –○–: structure=firewall.

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