Advances in acoustic eigenvalue analysis using boundary element method
Advances in acoustic eigenvalue analysis using boundary element method
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DOI：
10.1016/0045-7949(95)00012-6
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发表时间：
1995-09
影响因子：
4.7
通讯作者：
Ashraf Ali;C. Rajakumar;S. Yunus
中科院分区：
文献类型：
--
作者：
Ashraf Ali;C. Rajakumar;S. Yunus
本文回顾了边界元声学特征值分析的历史和发展。由于Helmholtz方程的自由空间绿色函数，声学本征值分析的控制微分方程，隐式地包含在其中的频率参数，通常的应用程序BE离散化这个方程并不自然地导致一个代数本征值问题。在过去，研究人员使用行列式搜索方法来寻找声学腔的谐振频率。后来，通过单独处理亥姆霍兹方程的惯性项，并使用绿色函数的拉普拉斯方程，这是免费的频率参数，它是可能的代数形式建立的声学本征值问题。因此，现在可以一次性形成相关矩阵以计算谐振频率。与有限元（FE）特征值问题相比，BE特征值公式导致更小的系统矩阵，因为离散仅限于边界。然而，BE公式涉及完全填充和非对称矩阵，需要特殊的特征值求解器。此外，一些声学本征值公式除了通常的边界离散化点外，还需要额外的域配置点，以准确评估本征频率，从而增加了问题的大小。用边界元法计算淹没在无限大流体中的结构的特征值是一个有待解决的问题。
A historical and critical review of the boundary element (BE) acoustic eigenvalue analysis is presented. Since the free-space Green's functions for the Helmholtz equation, the governing differential equation for acoustic eigenanalysis, implicitly contains the frequency parameter in them, the usual application of BE discretization to this equation does not naturally lead to an algebraic eigenvalue problem. In the past researchers have used the determinant search method to find resonant frequencies for acoustic cavities. Later on, by treating the inertial term of the Helmholtz equation separately and using Green's function for the Laplace's equation, which is free from the frequency parameter, it was possible to set up the acoustic eigenproblem in the algebraic form. As a result, the associated matrices could now be formed once and for all to compute the resonant frequencies. Compared to finite element (FE) eigenproblems, the BE eigenvalue formulations lead to smaller system matrices, since discretization is confined to the boundary only. However, the BE formulations involve fully populated and unsymmetric matrices, requiring special eigensolvers. Furthermore, some acoustic eigenvalue formulations require additional domain collocation points in addition to the usual boundary discretization points for an accurate evaluation of the eigenfrequencies, thereby increasing the problem size. The problem of computing eigenvalues using BEM for structures submerged in infinite-extent fluid is yet to be resolved.