Analytical approach for sound attenuation in perforated dissipative silencers with inlet/outlet extensions

The acoustic attenuation performance of perforated dissipative circular expansion chambers with inlet/outlet extensions is investigated. The eigenvalues and eigenfunctions of the sound field are analytically determined in the extended inlet/outlet circular ducts, upstream/downstream end annular dissipative chambers, and the central perforated dissipative expansion chamber. Utilizing the continuity conditions of velocity/pressure at the interfaces, the transmission loss is predicted by a two-dimensional analytical approach. For a specific configuration, such predictions are compared with both experiments and a three-dimensional computational solution based on the substructure boundary element technique, showing a reasonable agreement. The analytical results for the effect of the absorbent resistivity, duct porosity, and geometry on the acoustic attenuation performance are discussed in detail.