A new approach to the theory of acoustic multi-port networks with multimode wave and its application to muffler analysis

Abstract

The paper presents a new approach to the theory of acoustic multi-port networks assuming propagation of multimode wave through the system and applying the scattering matrix formalism. A procedure is proposed which can be applied to improve accuracy of results obtained when analysing acoustic mufflers of complex geometry or other systems composed of several sub-systems joined by duct-like elements. In what follows, the multi-port order is defined by the number of ducts and a selected cross-section of a duct transmitting multimode wave is called the multimode port. The main feature of the presented method is that it allows to analyse each sub-system as a separate multi-port. The scattering matrix representing two selected consecutive sub-systems having a common multimode port could be transformed according to the derived formulae which results in reducing the number of multimode ports by two. The source term can be present in each sub-system. By executing this procedure step by step, the scattering matrix of the whole system can be determined. To ensure good accuracy of final results, the scattering matrix of a discontinuity constituting a degenerated multi-port is calculated with the near field effects taken into account adjusting the number of cut-off modes included in the analysis to the specified continuity conditions at junctions. The next step consists in reduction of the dimension of the “near-field scattering matrix” to the matrix accounting only for cut-on modes propagating in the adjoined ducts. The main advantage and the novelty of the presented procedure is that it can be executed step by step and thus applied to mufflers of complex geometry never leading to the scattering matrix of troublesomely large dimensions and at the same time, ensuring significant accuracy of the obtained results. The proposed method was validated in two ways: by comparing its results with those published in the literature and applying it to some other example mufflers of complex geometry.