無限領域を考慮した3次元音場の数値計算の一手法

概要

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In this paper, a numerical method is derived for Helmholtz equations in unbounded domains of the type arising in the analysis of acoustic transmission system with radiation. The given problem on an unbounded domain is replaced by an approximate problem on bounded domain with an approximate radiation boundary condition on the artificial boundary. In order to obtain a reasonable solution, it is necessary to make this boundary sufficiently far from the sound source. The domain is divided by an internal boundary surrounding the source into two domains, Ω_1 adjacent to the source and Ω_2 adjacent to the external domain. In Ω_2, first the phase term e^<ikr> of the spherical wave is factored out of the solution and then the finite element method (f. e. m. ) is employed with non-uniform mesh sizes, and in Ω_1, the f. e. m. is employed directly with uniform mesh size. Since the behavior of the solution may be much different from that of the spherical wave in a domain close to the source, the direct application of the f. e. m. solves the problem with a smaller error, and the adoption of non-uniform mesh sizes results in a great reduction in the number of equations to be solved. This method is applied to the practical problems, 3-dimensional acoustic field analysis of a rectangular horn and that of a rectangular speaker cabinet, to get satisfactory results.
社団法人日本音響学会の論文
1984-12-01