Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis
Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis
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DOI：
10.1115/1.3269388
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发表时间：
1987
影响因子：
1.7
通讯作者：
A. Seybert;C. R. Cheng
中科院分区：
文献类型：
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作者：
A. Seybert;C. R. Cheng
本文讨论了边界元方法(BEM)在简约波(Helmholtz)方程描述的室内声学问题中的应用。在内部区域边界有效的积分方程式的发展遵循外部问题的类似公式，除了内部问题外，不调用Sommerfeld辐射条件。内部问题的边界积分方程解不存在与外部问题的边界积分方程列式相关的非唯一性困难。边界积分方程式一旦得到，就可以用二次等参面元对特定几何图形进行求解。对于轴对称空腔和边界条件的简化允许使用空腔生成器上的线单元来获得解。本公式包括可以将节点放置在边界上不存在唯一切平面的位置(例如，在边或角点处)的情况。对于两类经典的内部轴对称问题：空腔的声学响应和消声器的传递损失，证明了边界元的能力。对于空腔响应，通过解析解提供了比较数据。对于消声器问题，将边界元解与有限元分析得到的数据进行了比较。
This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.