The collocation-based impedance-to-scattering matrix method recently developed in conjunction with the boundary element method (BEM) for large silencer analysis is reformulated by using the reciprocal identity integral. The reciprocal identity integral also forms the foundation of the classical theory of acoustic reciprocity for silencers. Contrary to the conventional wisdom, when the inlet and the outlet of a large silencer are switched, the transmission loss (TL) may not remain the same at frequencies above the plane-wave cutoff of the inlet and outlet. Numerical results using the BEM as well as the finite element method (FEM) are provided to confirm the hypothesis. Some practical issues related to the application of the impedance-to-scattering matrix method are also investigated. One issue is on the combination of subsystems in series connection using the scattering matrices. It is found that the more stable Redheffer star product must be used instead of the simple matrix multiplication using the transfer scattering matrices. Another practical issue is on the modeling of large silencers with a ½ or a ¼ reflective symmetry. A more restrictive selection of modes must be used in place of the general complete modal expansion in cylindrical coordinates.

通过使用倒数恒等积分，重新构造了最近结合边界元素方法（BEM）进行大消声器分析的基于搭配的阻抗到散射矩阵方法。互惠身份积分也构成了消音器经典声学互惠理论的基础。与传统观点相反，当切换大型消音器的入口和出口时，在入口和出口的平面波截止点以上的频率处，传输损耗（TL）可能不会保持相同。提供了使用BEM以及有限元方法（FEM）进行的数值结果，以证实这一假设。还研究了与阻抗散射矩阵法的应用有关的一些实际问题。一个问题是使用散射矩阵将子系统串联连接的组合。发现必须使用更稳定的Redheffer星积，而不是使用转移散射矩阵的简单矩阵乘法。另一个实际问题是具有½或¼反射对称性的大型消音器的建模。必须使用更严格的模式选择来代替圆柱坐标中的一般完全模态展开。