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Research Papers

Modified Interval Perturbation Finite Element Method for a Structural-Acoustic System With Interval Parameters

[+] Author and Article Information
Baizhan Xia

e-mail: xiabzff@163.com

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.

Manuscript received April 15, 2012; final manuscript received November 7, 2012; accepted manuscript posted November 19, 2012; published online May 23, 2013. Assoc. Editor: Weinong Chen.

J. Appl. Mech 80(4), 041027 (May 23, 2013) (8 pages) Paper No: JAM-12-1157; doi: 10.1115/1.4023021 History: Received April 15, 2012; Revised November 07, 2012; Accepted November 19, 2012

For the frequency response analysis of the structural-acoustic system with interval parameters, a modified interval perturbation finite element method (MIPFEM) is proposed. In the proposed method, the interval dynamic equilibrium equation of the uncertain structural-acoustic system is established. The interval structural-acoustic dynamic stiffness matrix and the interval force vector are expanded by using the first-order Taylor series; the inversion of the invertible interval structural-acoustic dynamic stiffness matrix is approximated by employing a modified approximate interval-value Sherman–Morrison–Woodbury formula. The proposed method is implemented at an element-by-element level in the finite element framework. Numerical results on a shell structural-acoustic system with interval parameters verify the accuracy and efficiency of the proposed method.

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Figures

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Fig. 1

A coupled structural-acoustic model

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Fig. 2

Shell structural-acoustic model

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Fig. 3

The lower boundary values of the sound pressure distributing on the middle section at uncertain level α'=0.2: (a) MCM, (b) IPFEM, and (c) MIPFEM

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Fig. 4

The upper boundary values of the sound pressure distributing on the middle section at uncertain level α'=0.2: (a) MCM, (b) IPFEM, and (c) MIPFEM

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Fig. 5

The intervals of the sound pressure distributing along the top boundary line at uncertain level α'=0.05

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Fig. 6

The intervals of the sound pressure distributing along the top boundary line at uncertain level α'=0.1

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Fig. 7

The intervals of the sound pressure distributing along the top boundary line at uncertain level α'=0.2

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Fig. 8

The frequency response intervals of the node A1 at uncertain level α'=0.05

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Fig. 9

The frequency response intervals of the node A1 at uncertain level α'=0.1

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Fig. 10

The frequency response intervals of the node A1 at uncertain level α'=0.2

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