Side-branch resonators modelling with Green׳s function methods

This paper deals with strategies for computing efficiently the propagation of sound waves in ducts containing passive components. In many cases of practical interest, these components are acoustic cavities which are connected to the duct. Though standard Finite Element software could be used for the numerical prediction of sound transmission through such a system, the method is known to be extremely demanding, both in terms of data preparation and computation, especially in the mid-frequency range. To alleviate this, a numerical technique that exploits the benefit of the FEM and the BEM approach has been devised. First, a set of eigenmodes is computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. By choosing an appropriate Green׳s function for the duct, the integration procedure is limited to the duct–cavity interface only. This allows an accurate computation of the scattering matrix of such an acoustic system with a numerical complexity that grows very mildly with the frequency. Typical applications involving Helmholtz and Herschel–Quincke resonators are presented.