Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function
Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function
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DOI：
10.1007/s00466-002-0350-y
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发表时间：
2002-10
影响因子：
4.1
通讯作者：
Jeng-Tzong Chen;M. Chang;K. Chen;I. Chen
中科院分区：
文献类型：
--
作者：
Jeng-Tzong Chen;M. Chang;K. Chen;I. Chen
本文提出了一种基于配置法的任意形状声腔特征分析的理论公式。本文可以看作是Kang等人提出的无因次影响函数方法的推广。(1999,2000a)从二维扩展到三维情况。与文献中的传统配置方法不同，本文所用的近似函数是两点函数，其自变量仅为两点之间的距离。基于这种径向基展开式，可以更准确地表示声场。通过径向基函数的线性叠加得到场解，并在离散点上施加边界条件。无论腔体的边界形状如何，影响矩阵都是对称的，计算出的特征值只需几个边界节点即可快速收敛到精确值。此外，该方法还产生了真边界模和伪边界模，分别由奇异值分解的右、左么正向量得到。通过使用奇异值分解(SVD)的更新项和文档，可以分别区分真伪本征解。通过几个数值算例说明了该方法的有效性。
In this paper, a theoretical formulation based on the collocation method is presented for the eigenanalysis of arbitrarily shaped acoustic cavities. This article can be seen as the extension of non-dimensional influence function (NDIF) method proposed by Kang et al. (1999, 2000a) extending from two-dimensional to three-dimensional case. Unlike the conventional collocation techniques in the literature, approximate functions used in this paper are two-point functions of which the argument is only the distance between the two points. Based on this radial basis expansion, the acoustic field can be represented more exactly. The field solution is obtained through the linear superposition of radial basis function, and boundary conditions can be applied at the discrete points. The influence matrix is symmetric regardless of the boundary shape of the cavity, and the calculated eigenvalues rapidly converge to the exact values by using only a few boundary nodes. Moreover, the method results in true and spurious boundary modes, which can be obtained from the right and left unitary vectors of singular value decomposition, respectively. By employing the updating term and document of singular value decomposition (SVD), the true and spurious eigensolutions can be sorted out, respectively. The validity of the proposed method are illustrated through several numerical examples.