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Research Papers

Response Analysis of Acoustic Field With Convex Parameters

[+] Author and Article Information
Baizhan Xia

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China

Dejie Yu

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China
e-mail: djyu@hnu.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 28, 2013; final manuscript received April 26, 2014; published online June 2, 2014. Assoc. Editor: Liang-Wu Cai.

J. Vib. Acoust 136(4), 041017 (Jun 02, 2014) (12 pages) Paper No: VIB-13-1226; doi: 10.1115/1.4027631 History: Received June 28, 2013; Revised April 26, 2014

The acoustic field with convex parameters widely exists in the engineering practice. The vertex method and the anti-optimization method are not considered as appropriated approaches for the response analysis of acoustic field with convex parameters. The shortcoming of the vertex method is that the local optima out of vertexes cannot be identified. The disadvantage of the anti-optimization method is that the analytical formulation of response may be not obtained. To analyze the acoustic field with convex parameters efficiently and effectively, a first-order convex perturbation method (FCPM) and a second-order convex perturbation method (SCPM) are presented. In FCPM, the response of the acoustic field with convex parameters is expanded with the first-order Taylor series. In SCPM, the response of the acoustic field with convex parameters is expanded with the second-order Taylor series neglecting the nondiagonal elements of Hessian matrix. The variational bounds of the expanded responses in FCPM and SCPM are yielded by the Lagrange multiplier method. The accuracy and efficiency of FCPM and SCPM are investigated by numerical examples.

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Figures

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Fig. 1

An acoustic field model

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Fig. 3

The sound pressures of node R1 yielded by FEM at the mesh dimensions 100 mm × 50 mm, 50 mm × 50 mm, 25 mm × 25 mm, and 12.5 mm × 12.5 mm and the analytical solution of node R1

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Fig. 4

The bounds of the sound pressure along the central axis at the frequency of 100 Hz

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Fig. 5

The bounds of the sound pressure along the central axis at the frequency of 200 Hz

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Fig. 6

The bounds of the sound pressure along the central axis at the frequency of 300 Hz

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Fig. 7

The bounds of the sound pressure along the central axis at the frequency of 400 Hz

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Fig. 8

The acoustic cavity of a car

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Fig. 9

The bounds of the real part and the imaginary part of the sound pressure along the bottom boundary at the frequency of 200 Hz: (a) the real part of the sound pressure and (b) the imaginary part of the sound pressure

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Fig. 10

A 3D acoustic cavity

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Fig. 11

The bounds of the sound pressure along the top boundary line at the frequency of 300 Hz

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