A Generalized Infinite Element for Acoustic Radiation

Abstract

A generalized infinite element is presented by combining following aspects: (1) The geometry mapping in the Cartesian system is chosen so as to facilitate the generation of infinite element mesh; (2) The decay variable is defined as the in situ major axis of the confocal ellipse where the field point is located, so it is dependent not only on the infinite-directional coordinate but on the finite-directional one(s); (3) The shape function is constructed so that it exactly satisfies the multipole expansion along the edges of the infinite element; (4) The conjugated weighting function is adopted to eliminate the harmonic terms from the integrands; and (5) the more proper form of phase factor and weighting factor is recommended. Compared with the Bettess element and the Astley element, the present element greatly reduces the element number within the finite element zone for problems with a large aspect ratio. Compared with the Burnett element and the modified Burnett element, the present element permits the free orientation of the infinite element, and thereby is suitable for more general exterior problems, either of a closed surface (source) or of an opening surface (source). Several typical examples are given and their results show that the generalized infinite element is robust and flexible.

A Beam-Tracing Domain Decomposition Method for Sound Holography in Church Acoustics

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Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

“…A superior feature of the BEM is that it can deal with the exterior acoustics in an infinite domain. There have also been studies of infinite element types for the FEM to approximate the infinite domain (Li et al, 2005;Autrique and Magoules, 2006).…”

ADITU: A mesh-free formulation for the solution of Helmholtz equation in bounded and unbounded domains

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