Impedance-to-scattering matrix method for large silencers Part II: Integral formulation, acoustic reciprocity and practical issues

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.