ACOUSTIC BEHAVIOUR OF ELLIPTICAL CHAMBER MUFFLERS

The present work studies in detail the acoustic behaviour of mufflers with elliptical cross-section. The effect of the chamber length and the location of the inlet and outlet ports is considered. In addition, the eccentricity of the ellipse is taken into account, since it generates important discrepancies with respect to those results obtained for the case of circular chambers, mainly when practical values of eccentricity are considered. The analytical description of the acoustic behaviour of chambers with elliptical cross-section has been obtained via the truncated modal superposition method. First, the problem of natural frequencies and mode shapes has been approached by considering the Helmholtz equation in an elliptical domain, the solution of which can be expressed by means of Mathieu functions. Then, the frequency response functions of the muffler have been evaluated through truncated modal superposition. The results obtained are shown to compare well with those obtained from finite element calculations and experimental measurements. In addition, simple polynomial expressions have been developed in order to evaluate the cut-off frequency of concentric and non-concentric elliptical chambers, which is an important feature since higher order modes start to propagate without attenuation above this frequency. A simple polynomial expression is also developed to find the optimum location of the outlet port in order to extend the range of acoustic attenuation of the muffler. The influence of the geometry on the acoustic performance and the propagation of elliptic modes is studied for two configurations of interest, such as the expansion chamber and the reversing chamber muffler.