A finite element approach for the acoustic modeling of perforated dissipative mufflers with non-homogeneous properties

In this work, a finite element approach is presented for modelling sound propagation in perforated dissipative mufflers with non-homogeneous properties. The spatial variations of the acoustic properties can arise, for example, from uneven filling processes during manufacture and degradation associated with the flow of soot particles within the absorbent material. First, the finite element method is applied to the wave equation for a propagation medium with variable properties (outer chamber with absorbent material) and a homogeneous medium (central passage). For the case of a dissipative muffler, the characterization of the absorbent material is carried out by means of its equivalent complex density and speed of sound. To account for the spatial variations of these properties, a coordinate-dependent function is proposed for the filling density of the absorbent material. The coupling between the outer chamber and the central passage is achieved by using the acoustic impedance of the perforated central pipe, that relates the acoustic pressure jump and the normal velocity through the perforations. The acoustic impedance of the perforated central duct includes the influence of the absorbent material and therefore a spatial variation of the impedance is also taken into account. A detailed study is then presented to assess the influence of the heterogeneous properties and the perforated duct porosity on the acoustic attenuation performance of the muffler.