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Article

A Generalized Infinite Element for Acoustic Radiation

[+] Author and Article Information
L.-X. Li

MSSV, School of Civil Engineering and Mechanics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China

J.-S. Sun, H. Sakamoto

Technical Research Institute, AOKI Corporation, Kaname 36-1, Tsukuba, Ibaraki, 300-2622, Japan

J. Vib. Acoust 127(1), 2-11 (Mar 21, 2005) (10 pages) doi:10.1115/1.1855927 History: Received April 01, 2003; Revised March 05, 2004; Online March 21, 2005
Copyright © 2005 by ASME
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References

Bettess,  P., and Zienkiewicz,  O. C., 1977, “Diffraction and Refraction of Surface Waves Using Finite and Infinite Elements,” Int. J. Numer. Methods Eng., 11, pp. 1271–1290.
Zienkiewicz,  O. C., Bando,  K., Bettess,  P., Emson,  C., and Chiam,  T. C., 1985, “Mapped Infinite Elements for Exterior Wave Problems,” Int. J. Numer. Methods Eng., 21, pp. 1229–1251.
Gerdes,  K., 2000, “A Review of Infinite Element Methods for Exterior Helmholtz Problems,” J. Comput. Acoust., 8(1), pp. 43–62.
Bettess,  J. A., and Bettess,  P., 1998, “A New Mapped Infinite Wave Element for General Wave Diffraction Problems and Its Validation on the Ellipse Diffraction Problem,” Comput. Methods Appl. Mech. Eng., 164, pp. 17–48.
Astley,  R. J., and Macaulay,  G. J., 1994, “Mapped Wave Envelope Elements for Acoustical Radiation and Scattering,” J. Sound Vib., 170(1), pp. 97–118.
Burnett,  D. S., 1994, “A Three-Dimensional Acoustic Infinite Element Based on a Prolate Spheroidal Multipole Expansion,” J. Acoust. Soc. Am., 96(5), pp. 2798–2816.
Shirron,  J. J., and Dey,  S., 2002, “Acoustic Infinite Elements for Nonseparable Geometries,” Comput. Methods Appl. Mech. Eng., 191, pp. 4123–4139.
Li, L.-X., Sun, J.-S., and Sakamoto, H., 2003, “An Integration Technique in Burnett Infinite Element,” Proc. 2003 ASME International Mechanical Engineering Congress and Exposition, ASME, New York.
Li,  L.-X., Sun,  J.-S., and Sakamoto,  H., 2003, “On the Virtual Acoustical Source in Mapped Infinite Element,” J. Sound Vib., 261, pp. 945–951.
Shirron,  J. J., and Babuska,  I., 1998, “A Comparison of Approximate Boundary Conditions and Infinite Element Methods for Exterior Helholtz Problems,” Comput. Methods Appl. Mech. Eng., 164, pp. 121–139.
Demkowicz,  L., and Ihlenburg,  F., 2001, “Analysis of a Coupled Finite-Infinite Element Method for Exterior Helmholtz Problems,” Numerische Mathematik,88, pp. 43–73.
Cremers,  L., Fyfe,  K. R., and Coyette,  J. P., 1994, “A Variable-Order Infinite Acoustic Wave Envelope Element,” J. Sound Vib., 171(4), pp. 483–508.
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Dreyer,  D., and von Estorff,  O., 2003, “Improved Conditioning of Infinite Elements for Exterior Acoustics,” Int. J. Numer. Methods Eng., 58, pp. 933–953.

Figures

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The geometry of the Bettess element
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The typical mapped infinite element
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The radiation object and its enclosing surfaces: Sc—the enclosing circle; Se—the enclosing ellipse
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The nodes ordering of variable-order infinite element
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Illustration of numerical models used in the two-dimensional examples: (a) Model 0—the usual mesh: Corner nodes and midside nodes are generated through emanating from O(0,0) per 5 deg, (b) Model 1—corner nodes are generated through emanating from O(0,0) whereas midside nodes are generated through emanating from O(x0,0) per 5 deg, and (c) Model 2—corner nodes are generated through emanating from O(0,0) whereas midside nodes are generated as the points of the intersection between outer circle and rays emanating from O(x0,0) and passing through the corresponding corner point on the inner circle
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Results of second-order element when r2=2r1: The radiation of a dipole. (a) Results from the Astley element, and (b) Results from the present element.
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Results of second-order element when r2=3r1: The radiation of a dipole. (a) Results from the Astley element, and (b) Results from the present element.
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Results of third-order element when r2=2r1: The scattering of a circular cylinder. (a) Results from the Astley element, and (b) Results from the present element.
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Results of third-order element when r2=3r1: The scattering of a circular cylinder. (a) Results from the Astley element, and (b) Results from the present element.
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The illustration of the mesh used in the axisymmetric example: (a) Model 3 (fMesh=0), and (b) Model 4 (fMesh=D/2)
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Comparison of results using Model 3 (fCal=3D/8): (a) Results of third-order element for kD=4π, (b) Results of fourth-order element for kD=6π, and (c) Results of fifth-order element for kD=8π
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Comparison of results using Model 4 (fCal=3D/8): (a) Results of third-order element for kD=4π, (b) Results of fourth-order element for kD=6π, and (c) Results of fifth-order element for kD=8π
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Results of fifth-order element for kD=8π (fMesh=D/2)
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Comparison of results using variable model (fMesh=fCal=3D/8): (a) Results of third-order element for kD=4π, (b) Results of fourth-order element for kD=6π, and (c) Results of fifth-order element for kD=8π

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