Boundary element analysis of bar silencers using the scattering matrix with two-dimensional finite element modes

Bar silencers used in industry may consist of a large array of rectangular or round bars packed in a rectangular lattice arrangement. Due to the size of the lattice, normally only a single unit that represents a building block for the lattice is isolated for analysis purposes. Even with one isolated unit, the inlet and the outlet are still quite large, and the plane-wave cutoff frequency can be very low. Therefore, higher-order modes must be considered at the inlet and outlet in order to calculate the transmission loss. This paper uses the recently developed “impedance-to-scattering matrix method” to convert the element-based impedance matrix into the mode-based scattering matrix for transmission loss calculation. Depending on the shape of the inlet and outlet, it may not always be possible to find an analytical expression of the modes needed for the modal expansion. In this paper, the two-dimensional finite element method is used to extract the eigenvalues and the eigenvectors of the inlet/outlet cross section. The eigenvectors are then used in the modal expansion to convert the impedance matrix into the scattering matrix. Test cases include several commonly used inlet and outlet configurations, such as rectangular, circular and triangular cross sections.