Green's function approach for the transmission loss of concentrically multi-layered circular dissipative chamber

An analytical method has been proposed by using Green's function analysis to find the transmission loss (TL) of a concentrically multi-layered circular dissipative chamber. Each layer of the chamber is filled with a porous acoustic absorptive material and is separated from the adjacent one by a thin perforated screen. A tailored Green's function for this configuration, in the absence of mean flow, is expressed as the summation of eigenfunctions of the central duct. In the analysis, the walls of the chamber are assumed to be acoustically rigid. The cumulative effect of the layers has been incorporated in terms of the reflection coefficient in the eigenfunctions of the central duct. By using the piston analogy approach at the inlet and outlet ports of the chamber, the total velocity potential generated inside the central duct is estimated. Thence, the transfer matrix is evaluated to predict the TL. The results obtained from the current method are in good agreement with the numerical models and available literature. A parametric study has been conducted to investigate the effect of the number of layers, and their arrangement with respect to thickness and flow resistivity, on the acoustic performance of the chamber.