Research Papers

Component Mode Synthesis Method Applied to Two-Dimensional Acoustic Analysis in Ducts

[+] Author and Article Information
Maria Alzira de Araújo Nunes

University of Brasilia,
UnB Gama College,
Área Especial de Indústria Projeção A-UnB,
Setor Leste, 72444-240,
Gama-DF, Brazil
e-mail: maanunes@unb.br

Marcus Antônio Viana Duarte

Federal University of Uberlândia,
Mechanical Engineering College,
João Naves de Ávila Avenue, 2121,
Campus Santa Mônica,
Bloco 1M, 38400-902,
Uberlândia-MG, Brazil
e-mail: mvduarte@mecanica.ufu.br

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATIONAND ACOUSTICS. Manuscript received January 10, 2012; final manuscript received May 28, 2012; published online February 4, 2013. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 135(1), 011016 (Feb 04, 2013) (10 pages) Paper No: VIB-12-1014; doi: 10.1115/1.4007243 History: Received January 10, 2012; Revised May 28, 2012

This paper presents a modal approach to calculate the acoustic normal modes in complex ducts. In this study, the component modal synthesis (CMS) method in two dimensions for application in large duct with acoustic propagation in order to obtain a reduced acoustic model will be developed. The proposed technique is based on division of the acoustic system in well-known modal model subdomains and uses a CMS procedure to obtain a reduced acoustic modal model of the large system. In this paper, the applicability of the CMS Craig-Chang's method was adapted for acoustics CMS, considering only acoustic fluid interaction. In the modal synthesis technique developed originally for structural purpose, displacements and forces were coupled at the boundary of the substructures by dynamic constraint equations. The methodology developed here is based on residual flexibility, using residual inertia relief attachment modes in place of simply residual attachment modes to couple sound pressure and flow rates at the substructures interfaces. The approach leads to a versatile method with a low computational cost. To validate the proposed CMS approach, comparison with acoustic ducts models using finite element methodology (FEM) and analytical solutions were made. The differences between the analytical and numerical results as well as the limitations and advantages of each method were discussed.

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Fig. 1

Model 1: Two substructures (each substructure corresponds to a duct with closed ends) that results in a single duct with closed ends

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Fig. 2

Model 2: Two substructures (each substructure corresponds to a duct with closed ends) that results in a duct with closed ends and an internal partition plate

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Fig. 3

Closed rectangular volume representing a duct with both ends closed

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Fig. 4

Substructures (a) and (b) discretized and linked by a common interface

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Fig. 5

Flow chart of the CMS methodology proposed

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Fig. 6

Acoustic mode for the frequency of 26.38 Hz. (a) CMS model; (b) analytical model.

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Fig. 7

Acoustic mode for the frequency of 52.76 Hz. (a) CMS model; (b) analytical model.

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Fig. 8

Acoustic mode for the frequency of 131.92 Hz. (a) CMS model; (b) analytical model.

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Fig. 9

Dimensions adopted for the second model (with an internal plate of 1 mm thickness)

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Fig. 10

Acoustic mode for the frequency of 39.57 Hz. (a) CMS model; (b) FEM model.

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Fig. 11

Acoustic mode for the frequency near 132 Hz. (a) CMS model; (b) FEM model.

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Fig. 12

Acoustic mode for the frequency near 177 Hz. (a) CMS model; (b) FEM model.




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