School of Engineering and Architecture, Lucerne University, Technikumstrasse 21, CH-6048 Horw, Switzerland.
J Acoust Soc Am. 2013 Jul;134(1):292-9. doi: 10.1121/1.4807508.
A method for determining the complete higher-order scattering matrix of an acoustic discontinuity is developed. The method is demonstrated for a right-angled waveguide bend, and the magnitude and phase of the reflection and transmission coefficients are extracted precisely. The procedure is straightforward and based on the solutions to the Helmholtz equation by the finite element method (FEM). The consistency of the scattering coefficients found by this method is verified by their properties of symmetry, and their accuracy is established by the conservation of energy. The reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct FEM response to the reflection matrix calculation. Some features of the scattering matrix as a function of frequency are surprising, such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave. The methodology detailed in this paper can be extended to other multiport junctions, such as T-junctions or size discontinuities in ducts.
提出了一种确定声学不连续性完全高阶散射矩阵的方法。该方法针对直角波导弯管进行了演示，精确提取了反射和透射系数的幅度和相位。该过程简单直接，基于有限元法（FEM）求解亥姆霍兹方程。通过散射系数的对称性质验证了该方法所得散射系数的一致性，并通过能量守恒验证了其准确性。通过任意声源和将直接有限元响应与反射矩阵计算进行比较，进一步证明了新技术的可靠性。散射矩阵作为频率函数的某些特征令人惊讶，例如相位演化的阶跃和反转，或者入射波的完全传输损失。本文详细介绍的方法可以扩展到其他多端口接头，例如 T 型接头或管道中的尺寸不连续性。
