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Research Papers

Probabilistic Interval Perturbation Methods for Hybrid Uncertain Acoustic Field Prediction

[+] Author and Article Information
Baizhan Xia

e-mail: xiabzff@163.com

Dejie Yu

e-mail: djyu@hnu.edu.cn

Jian Liu

e-mail: liujian0108@vip.163.com
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan,
People's Republic of China, 410082

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received May 20, 2012; final manuscript received November 14, 2012; published online February 25, 2013. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 135(2), 021009 (Feb 25, 2013) (12 pages) Paper No: VIB-12-1156; doi: 10.1115/1.4023054 History: Received May 20, 2012; Revised November 14, 2012

For the hybrid uncertain acoustic field prediction with random and interval variables, the random interval dynamic equilibrium equation is established and two hybrid probabilistic interval perturbation methods, named as hybrid perturbation Monte Carlo method (HPMCM) and hybrid perturbation vertex method (HPVM), are present. In HPMCM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and Monte Carlo method. In HPVM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and the vertex method. Numerical results on a 2D acoustic tube, the 2D acoustic cavity of a car and a 3D acoustic cavity verify the effectiveness and the high efficiency of HPVM when compared with HPMCM. HPVM can be considered as an effective engineering method to quantify the effects of parametric uncertainty on the sound pressure response.

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Figures

Grahic Jump Location
Fig. 1

An acoustic cavity model

Grahic Jump Location
Fig. 3

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part calculated by HPMCM and HPVM at the leftmost point of the central axis (f = 300 Hz): (a) the upper bounds of expectation; (b) the lower bounds of expectation; (c) the upper bounds of variance; (d) the lower bounds of variance

Grahic Jump Location
Fig. 4

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part along the central axis calculated by HPMCM and HPVM at frequency f = 100 Hz: (a) the lower and upper bounds of expectation; (b) the lower and upper bounds of variance

Grahic Jump Location
Fig. 5

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part along the central axis calculated by HPMCM and HPVM at frequency f = 200 Hz: (a) the lower and upper bounds of expectation; (b) the lower and upper bounds of variance

Grahic Jump Location
Fig. 6

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part along the central axis calculated by HPMCM and HPVM at frequency f = 300 Hz: (a) the lower and upper bounds of expectation; (b) the lower and upper bounds of variance

Grahic Jump Location
Fig. 7

The 2D finite element mesh model of the acoustic cavity of a car

Grahic Jump Location
Fig. 8

The lower and upper bounds of expectation of the sound pressure's real and imaginary parts at node R1 in the frequency range f = 50–200 Hz: (a) the expectation of the sound pressure's real part; (b) the expectation of the sound pressure's imaginary part

Grahic Jump Location
Fig. 9

The lower and upper bounds of variance of the sound pressure's real and imaginary parts at node R1 in the frequency range f = 50–200 Hz: (a) the variance of the sound pressure's real part; (b) the variance of the sound pressure's imaginary part

Grahic Jump Location
Fig. 10

The lower and upper bounds of expectation of the sound pressure's real and imaginary parts at node R2 in the frequency range f = 50–200 Hz: (a) the expectation of the sound pressure's real part; (b) the expectation of the sound pressure's imaginary part

Grahic Jump Location
Fig. 11

The lower and upper bounds of variance of the sound pressure's real and imaginary parts at node R2 in the frequency range f = 50–200 Hz: (a) the variance of the sound pressure's real part; (b) the variance of the sound pressure's imaginary part

Grahic Jump Location
Fig. 12

A 3D acoustic cavity

Grahic Jump Location
Fig. 13

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part along the top boundary calculated by HPMCM and HPVM for f = 150 Hz: (a) the lower and upper bounds of expectation; (b) the lower and upper bounds of variance

Grahic Jump Location
Fig. 14

The lower and upper bounds of expectation and variance of the sound pressure's imaginary part along the top boundary calculated by HPMCM and HPVM for f = 300 Hz: (a) the lower and upper bounds of expectation; (b) the lower and upper bounds of variance

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