Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method
Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method
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DOI：
10.1016/j.enganabound.2013.03.015
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发表时间：
2013-06-01
影响因子：
3.3
通讯作者：
Isakari, Hiroshi
中科院分区：
文献类型：
--
作者：
Gao, Haifeng;Matsumoto, Toshiro;Isakari, Hiroshi
本文用边界元方法给出了三维声腔非线性特征值分析的精确数值解。为了求解边界元所描述的非线性特征值问题，我们采用了一种称为块Sakurai-Sugiura(SS)方法的轮廓积分方法，将NEP转化为一个标准的线性特征值问题，从而降低了特征空间的维度。本文所采用的分块方法也可以提取重数大于1的特征值，但对于包含内闭边界的复杂连通区域，该方法会产生虚拟的特征值。通过对具有唯一齐次边界条件的球体、具有混合边界条件的立方体以及由三次边界和球面边界组成的复杂连通区域的特征值计算，说明了该方法的应用，而虚拟的特征值可以用Burton-Miller方法识别。这些数值结果得到了适当的收敛研究和与封闭形式的比较的支持。(C)2013爱思唯尔有限公司。保留所有权利。
This paper presents accurate numerical solutions for nonlinear eigenvalue analysis of three-dimensional acoustic cavities by boundary element method (BEM). To solve the nonlinear eigenvalue problem (NEP) formulated by BEM; we employ a contour integral method, called block Sakurai-Sugiura (SS) method, by which the NEP is converted to a standard linear eigenvalue problem and the dimension of eigenspace is reduced. The block version adopted in present work can also extract eigenvalues whose multiplicity is larger than one, but for the complex connected region which includes a internal closed boundary, the methodology yields fictitious eigenvalues. The application of the technique is demonstrated through the eigenvalue calculation of sphere with unique homogenous boundary conditions, cube with mixed boundary conditions and a complex connected region formed by cubic boundary and spherical boundary, however, the fictitious eigenvalues can be identified by Burton-Miller's method. These numerical results are supported by appropriate convergence study and comparisons with close form. (C) 2013 Elsevier Ltd. All rights reserved.