The reactive attenuation of rectangular plenum chambers

Abstract

A mathematical formulation for evaluating the acoustic performance of plenum chambers is derived by using the eigenfunction expansion technique. The chamber is modelled as a piston-driven rectangular rigid tube with no losses and containing a medium otherwise at rest. The residual acoustic velocity potential in the chamber is obtained by superposing the three-dimensional velocity potentials due to each of the uniformly fluctuating pistons. All the geometrical parameters such as the size of the chamber and ports, the arbitrary locations of inlet/outlet ports and the shapes of the ports are taken into consideration in the formulation as well as the acoustic higher order modes generated at the area discontinuities of port-chamber interfaces. By using the derived 2 × 2 transfer matrices, any type of reactive rectangular plenum chamber including the throughflow, flow-reversal, Helmholtz resonator and end-in/side-out configurations can be characterized, and their insertion or transmission losses can be estimated very easily through the appropriate truncation of acoustic modal series. Computed values are compared with those predicted by the foregoing numerical methods and by the classical plane wave theory, and the former agree very well with the results of the present study. In addition, 90° and 180° duct bends are analyzed and the results are in good agreement with previous experimental ones. The derived transfer matrices can be easily incorporated as basic modules in any existing computer programs incorporating four-pole parameters for predicting the acoustic performance of silencing systems.