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Research Papers

Response Probability Analysis of Random Acoustic Field Based on Perturbation Stochastic Method and Change-of-Variable Technique

[+] Author and Article Information
Dejie Yu

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

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 8, 2012; final manuscript received June 4, 2013; published online July 5, 2013. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 135(5), 051032 (Jul 05, 2013) (11 pages) Paper No: VIB-12-1313; doi: 10.1115/1.4024853 History: Received November 08, 2012; Revised June 04, 2013

To calculate the probability density function of the response of a random acoustic field, a change-of-variable perturbation stochastic finite element method (CVPSFEM), which integrates the perturbation stochastic finite element method (PSFEM) and the change-of-variable technique in a unified form, is proposed. In the proposed method, the response of a random acoustic field is approximated as a linear function of the random variables based on a first order stochastic perturbation analysis. According to the linear relationship between the response and the random variables, the formal expression of the probability density function of the response of a random acoustic field is obtained by the change-of-variable technique. The numerical examples on a two-dimensional (2D) acoustic tube and a three-dimensional (3D) acoustic cavity of an automobile cabin verify the accuracy and efficiency of the proposed method. Hence, the proposed method can be considered as an effective method to quantify the effects of the parametric randomness of a random acoustic field on the sound pressure response.

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References

Figures

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Fig. 1

Acoustic cavity model

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Fig. 3

Probability densities of the imaginary part of the sound pressure along the central axis calculated by CVPSFEM at a frequency f = 50 Hz

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Fig. 4

Probability densities of the imaginary part of the sound pressure along the central axis calculated by the Monte Carlo method at a frequency f = 50 Hz

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Fig. 5

Probability densities of the imaginary part of the sound pressure at nodes R1 and R2 calculated by CVPSFEM and the Monte Carlo method at frequency f = 50 Hz: (a) probability densities of node R1 and (b) probability densities of node R2

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Fig. 6

Probability densities of the imaginary part of the sound pressure at nodes R1 and R2 calculated by CVPSFEM and the Monte Carlo method at frequency f = 100 Hz: (a) probability densities of node R1 and (b) probability densities of node R2

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Fig. 7

Probability densities of the imaginary part of the sound pressure at nodes R1 and R2 calculated by CVPSFEM and the Monte Carlo method at frequency f = 200 Hz: (a) probability densities of node R1 and (b) probability densities of node R2

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Fig. 8

Probability densities of the imaginary part of the sound pressure at nodes R1 and R2 calculated by CVPSFEM and the Monte Carlo method at the interested value − 100 Pa: (a) probability densities of node R1 and (b) probability densities of node R2

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Fig. 9

Probability densities of the imaginary part of the sound pressure at nodes R1 and R2 calculated by CVPSFEM and the Monte Carlo method at the interested value 100 Pa: (a) probability densities of node R1 and (b) probability densities of node R2

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Fig. 10

Expectations and standard variances of the imaginary part of the sound pressure along the central axis calculated by CVPSFEM, PSFEM, and the Monte Carlo method at frequency f = 50 Hz: (a) expectations and (b) standard variances

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Fig. 11

Expectations and standard variances of the imaginary part of the sound pressure along the central axis calculated by CVPSFEM, PSFEM, and the Monte Carlo method at frequency f = 100 Hz: (a) expectations and (b) standard variances

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Fig. 12

Expectations and standard variances of the imaginary part of the sound pressure along the central axis calculated by CVPSFEM, PSFEM, and the Monte Carlo method at frequency f = 200 Hz: (a) expectations and (b) standard variances

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Fig. 13

3D acoustic cavity of an automobile cabin

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Fig. 14

Probability densities of the imaginary part of the sound pressure at nodes G1 and G2 calculated by CVPSFEM and the Monte Carlo method at frequency f = 50 Hz: (a) probability densities of node G1 and (b) probability densities of node G2

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Fig. 15

Probability densities of the imaginary part of the sound pressure at nodes G1 and G2 calculated by CVPSFEM and the Monte Carlo method at frequency f = 100 Hz: (a) probability densities of node G1 and (b) probability densities of node G2

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Fig. 16

Probability densities of the imaginary part of the sound pressure at nodes G1 and G2 calculated by CVPSFEM and the Monte Carlo method at the interested value 30 Pa: (a) probability densities of node G1 and (b) probability densities of node G2

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