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Research Papers

Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method

[+] Author and Article Information
L. Y. Yao

College of Engineering and Technology,
Southwest University,
No. 2 Tiansheng Road,
BeiBei District, Chongqing 400715, China
e-mail: 19831022y@163.com

J. W. Zhou

China Automotive Engineering
Research Institute Co. Ltd.,
No. 9 Jinyu Avenue,
New North Zone, Chongqing 401122, China
e-mail: 121162893@qq.com

Z. Zhou

China Automotive Engineering
Research Institute Co. Ltd.,
No. 9 Jinyu Avenue,
New North Zone, Chongqing 401122, China
e-mail: 3099236590@qq.com

L. Li

College of Engineering and Technology,
Southwest University,
No. 2 Tiansheng Road,
BeiBei District, Chongqing 400715, China
e-mail: cqulily@163.com

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 14, 2013; final manuscript received November 11, 2014; published online January 20, 2015. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 137(2), 021013 (Apr 01, 2015) (8 pages) Paper No: VIB-13-1240; doi: 10.1115/1.4029160 History: Received July 14, 2013; Revised November 11, 2014; Online January 20, 2015

The shape function of the finite element-least square point interpolation method (FE-LSPIM) combines the quadrilateral element for partition of unity and the least square point interpolation method (LSPIM) for local approximation, and inherits the completeness properties of meshfree shape functions and the compatibility properties of FE shape functions, and greatly reduces the numerical dispersion error. This paper derives the formulas and performs the dispersion analysis for the FE-LSPIM. Numerical results for benchmark problems show that, the FE-LSPIM yields considerably better results than the finite element method (FEM) and element-free Galerkin method (EFGM).

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Figures

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Fig. 1

Definition of nodal supports and element support. Nodal supports are defined as Ω1= {1, 2, 3, 4, 5, 6, 7, 8, 9}, Ω2= {1, 2, 3, 4, 8, 9, 10, 11, 12}, Ω3= {1, 2, 3, 4, 11, 12, 13, 14, 15}, and Ω4= {1, 2, 3, 4, 5, 6, 14, 15, 16}. The element support is defined as Ω=Ω1⊕Ω2⊕Ω3⊕Ω4= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}.

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Fig. 2

Illustration of nodes used for constructing system equations associated with node S(i, j): (a) FEM, (b) EFGM, and (c) FE-LSPIM

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Fig. 3

Dispersion error over θ and kh for FEM, EFGM, and FE-LSPIM using regular triangular mesh: (a) FEM, (b) EFGM, and (c) FE-LSPIM

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Fig. 4

Comparison on the dispersion error for different wave-numbers obtained using the FE-LSPIM, the EFGM, and the FEM: (a) kh = 1, (b) kh = 1.5, and (c) kh = 2

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Fig. 5

Comparison on the dispersion error for different wave-numbers at certain wave propagation angle

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Fig. 6

Comparison of sensitivity for different nondimensional wave-number for the FE-LSPIM, the EFGM, and the FEM

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Fig. 7

Comparison of convergence for maximum of dispersion error for different wave-numbers for the FE-LSPIM, the EFGM, and the FEM

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