0
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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Harari, I., 2006, “A Survey of Finite Element Methods for Time-Harmonic Acoustics,” Comput. Methods Appl. Mech. Eng., 195(13–16), pp. 1594–1607. [CrossRef]
James, K. R., and Dowling, D. R., 2008, “A Method for Approximating Acoustic-Field-Amplitude Uncertainty Caused by Environmental Uncertainties,” J. Acoust. Soc. Am., 124(3), pp. 1465–1476. [CrossRef] [PubMed]
Heaney, K. D., and Cox, H., 2006, “A Tactical Approach to Environmental Uncertainty and Sensitivity,” IEEE J. Ocean. Eng., 31(2), pp. 356–367. [CrossRef]
Finette, S., 2009, “A Stochastic Response Surface Formulation of Acoustic Propagation Through an Uncertain Ocean Waveguide Environment,” J. Acoust. Soc. Am., 126(5), pp. 2242–2247. [CrossRef] [PubMed]
Khine, Y. Y., Creamer, D. B., and Finette, S., 2010, “Acoustic Propagation in an Uncertain Waveguide Environment Using Stochastic Basis Expansions,” J. Comput. Acoust., 18(4), pp. 397–441. [CrossRef]
James, K. R., and Dowling, D. R., 2011, “Pekeris Waveguide Comparisons of Methods for Predicting Acoustic Field Amplitude Uncertainty Caused by a Spatially Uniform Environmental Uncertainty (L),” J. Acoust. Soc. Am., 129(3), pp. 589–592. [CrossRef] [PubMed]
Hayward, T. J., and Dhakal, S., 2012, “Acoustic Field and Array Response Uncertainties in Stratified Ocean Media,” J. Acoust. Soc. Am., 132(1), pp. 56–68. [CrossRef] [PubMed]
Stefanou, G., 2009, “The Stochastic Finite Element Method: Past, Present and Future,” Comput. Methods Appl. Mech. Eng., 198(9–11), pp. 1031–1051. [CrossRef]
Adhikari, S., 2011, “Doubly Spectral Stochastic Finite–Element Method for Linear Structural Dynamics,” ASCE J. Aerosp. Eng., 24(2), pp. 264–276. [CrossRef]
Tootkaboni, M., Asadpoure, A., and Guest, J. K., 2012, “Topology Optimization of Continuum Structures Under Uncertainty—A Polynomial Chaos Approach,” Comput. Methods Appl. Mech. Eng., 201–204, pp. 263–275. [CrossRef]
Sarrouy, E., Dessombz, O., and Sinou, J. J., 2012, “Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion—Application to a Finite Element Rotor,” ASME J. Vib. Acoust., 134(5), p. 051009. [CrossRef]
Doltsinis, I., and Kang, Z., 2006, “Perturbation-Based Stochastic FE Analysis and Robust Design of Inelastic Deformation Processes,” Comput. Methods Appl. Mech. Eng., 199(19–22), pp. 2231–2251. [CrossRef]
Kamínski, M., 2008, “On Stochastic Finite Element Method for Linear Elastostatics by the Taylor Expansion,” Struct. Multidiscip. Optimiz., 35(3), pp. 213–223. [CrossRef]
Ichchou, M. N., Bouchoucha, F., Ben Souf, M. A., Dessombz, O., and Haddar, M., 2011, “Stochastic Wave Finite Element for Random Periodic Media Through First-Order Perturbation,” Comput. Methods Appl. Mech. Eng., 200(41–44), pp. 2805–2813. [CrossRef]
Dash, P., and Singh, B. N., 2012, “Geometrically Nonlinear Free Vibration of Laminated Composite Plate Embedded With Piezoelectric Layers Having Uncertain Material Properties,” ASME J. Vib. Acoust., 134(6), p. 061006. [CrossRef]
Kamínski, M., 2012, “Probabilistic Entropy in Homogenization of the Periodic Fiber-Reinforced Composites With Random Elastic Parameters,” Int. J. Numer. Methods Eng., 90(8), pp. 939–954. [CrossRef]
Lazarov, B. S., Schevenels, M., and SigmundO., 2012, “Topology Optimization With Geometric Uncertainties by Perturbation Techniques,” Int. J. Numer. Methods Eng., 90(11), pp. 1321–1336. [CrossRef]
Rong, B., Rui, X., and Tao, L., 2012, “Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures,” ASME J. Appl. Mech., 79(2), p. 021005. [CrossRef]
Kamínski, M., and Solecka, M., 2013, “Optimization of the Truss-Type Structures Using the Generalized Perturbation-Based Stochastic Finite Element Method,” Finite Elem. Anal. Des., 63, pp. 69–79. [CrossRef]
Culla, A., and Carcaterra, A., 2007, “Statistical Moments Predictions for a Moored Floating Body Oscillating in Random Waves,” J. Sound Vib., 308(1–2), pp. 44–66. [CrossRef]
Hua, X. G., Ni, Y. Q., Chen, Z. Q., and Ko, J. M., 2007, “An Improved Perturbation Method for Stochastic Finite Element Model Updating,” Int. J. Numer. Methods Eng., 73(13), pp. 1845–1864. [CrossRef]
Panayirci, H. M., and Schuëller, G. I., 2011, “On the Capabilities of the Polynomial Chaos Expansion Method Within SFE Analysis—An Overview,” Arch. Comput. Methods Eng., 18(1), pp. 43–55. [CrossRef]
Papadimitriou, C., Katafygiotis, L. S., and Beck, J. L., 1995, “Approximate Analysis of Response Variability of Uncertain Linear Systems,” Prob. Eng. Mech., 10(4), pp. 251–264. [CrossRef]
Papoulis, A., and Pillai, S. U., 2002, Probability, Random Variables and Stochastic Processes, McGraw-Hill, Boston.
Kleiber, M., and Hien, T. D., 1992, The Stochastic Finite Element Method, John Wiley, New York.

Figures

Grahic Jump Location
Fig. 1

Acoustic cavity model

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 13

3D acoustic cavity of an automobile cabin

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In