Rayleigh–Ritz approach for predicting the acoustic performance of lined rectangular plenum chambers

The purpose of this study was to predict the acoustic performance of a fully lined rectangular plenum chamber having inlet and outlet ports at arbitrary locations. Because no exact analytic solution exists for this reactive-resistive silencer configuration, numerical methods are only available for a three-dimensional analysis. The lined plenum chamber was modeled as a piston-driven rectangular tube without mean flow and the acoustic pressure in the lined chamber was obtained by superposing the acoustic pressures due to each harmonically fluctuating piston. Air pore and skeleton material of the porous liner was reduced to an equivalent medium; thus, its acoustic characteristic was given by bulk-reacting liner properties. A single weak variational statement, which satisfies the conditions of the oscillating piston and all necessary boundary conditions, was developed. The Rayleigh-Ritz method was employed as the numerical scheme for the derived variational statement. Using a transfer matrix and measured material properties, all possible types of lined plenum chambers were tested. Computed results were compared with the predicted transmission loss by the locally reacting liner model and experimental results. Transmission loss predicted by the Rayleigh–Ritz method using the bulk-reacting liner model agreed well with the measured one.