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Research Papers

Analyzing Acoustic Radiation Modes of Baffled Plates With a Fast Multipole Boundary Element Method

[+] Author and Article Information
Haijun Wu

e-mail: wkjiang@sjtu.edu.cn

Weikang Jiang

e-mail: navy_wu@sjtu.edu.cn
State Key Laboratory of Mechanical System and Vibration
Shanghai Jiao Tong University,
Shanghai 200240, China

Yijun Liu

Mechanical Engineering,
University of Cincinnati,
Cincinnati, OH 45221-0072
e-mail: Yijun.Liu@uc.edu

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 9, 2011; final manuscript received May 24, 2012; published online February 4, 2013. Assoc. Editor: Lonny Thompson.

1Corresponding author.

J. Vib. Acoust 135(1), 011007 (Feb 04, 2013) (7 pages) Paper No: VIB-11-1174; doi: 10.1115/1.4007023 History: Received August 09, 2011; Revised May 24, 2012

In the analysis of an acoustic radiation mode of a baffled plate, Rayleigh integral with free space Green's function is involved. The boundary element method (BEM) is one of the approaches to compute its modes and radiation efficiencies. In this paper a fast multipole BEM in conjunction with an iterative solver based on the implicit restart Arnold method is proposed to efficiently and accurately evaluate acoustic radiation modes and efficiencies. Even though a 3D free space Green's function is used here, a quad tree is used for the hierarchical tree structure of the boundary mesh instead of an oct tree, which can speed up the fast multipole BEM. Similar to the analytical integration of moment evaluations, the analytical integration is also employed to compute the local expansion coefficients which further improves the efficiency of the fast multipole BEM for the analysis of an acoustic radiation mode of baffled plates. Comparison between numerical and theoretical radiation efficiencies of a baffled circular plate vibrating as a piston shows that the fast multipole BEM proposed here can give results with very good accuracy. The computation of the eigenvalues and eigenvectors of a baffled rectangular plate further reveals the efficiency in CPU time, smaller memory size, and accuracy of the fast multipole BEM in the analysis of an acoustic radiation mode.

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Figures

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Fig. 1

Tree structure of a plate model by using (a) an oct tree and (b) a quad tree

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Fig. 2

(a) Radiation efficiency of a baffled circular plate calculated numerically and theoretically and (b) the relative errors

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Fig. 3

The first six radiation modes of a rectangular plate

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Fig. 4

CPU time of the direct BEM and fast multipole BEM

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