THE TRANSFER MATRIX FOR A DISSIPATIVE SILENCER OF ARBITRARY CROSS-SECTION

In this work, the acoustic transfer matrix for a cylindrical dissipative silencer of arbitrary cross-section and bulk-reacting lining is derived for the case of negligible mean flow. The derivation is performed in a two-step procedure. First, the corresponding infinite-lined duct is analyzed by separating the longitudinal dependence and using collocation for the entailing eigenvalue problem. Then, using the resulting eigenmodes, the acoustic field in the silencer is expanded and adjusted to the boundary conditions at the in/outlet by mode-matching. To illustrate the applicability and numerical efficiency of the proposed technique a practical example is given.