3. Characterization of an Elliptical Chamber Muffler

This chapter presents a 3-D semi-analytical approach to characterize a single-inlet and single-outlet (SISO) rigid-wall elliptical (circular) cylindrical chamber muffler having arbitrary port location and evaluate its transmission loss (TL) performance. First, the acoustic pressure field inside an elliptical cylindrical cavity is expressed as modal summation in terms of the angular and radial Mathieu functions and the circular functions. Solving the inhomogeneous Helmholtz equation based on modeling the ports as a point-source, and using the modal expansion, one obtains the 3-D Green’s function acoustic pressure response function. The Green’s function response is then integrated over the end or side ports which are now modeled as rigid oscillating pistons (and divided by their cross-sectional area) to obtain the acoustic pressure response based on the uniform piston-driven model. This yields the impedance [Z] matrix parameters of different elliptical muffler configurations, namely end-inlet and end-outlet as well as end-inlet and side-outlet configuration. Additionally, the analytical formulation enables one to examine the influence of location of the end/side ports on the suppression (or excitation) of a given transverse mode type; this insight will be used for designing short mufflers in the ensuing chapter. Finally, we present an expression for TL in terms of [Z] matrix parameters which is particularly suited to explain and predict the attenuation peak or trough features.