This book presents a three-dimensional analysis of acoustic wave propagation in an elliptical
waveguide and applies the equations and concepts to design axially short elliptical
end-chamber muffler configurations which are an important component of a complex multi-pass
muffler used in a modern-day automotive exhaust system. A general solution of the Helmholtz
equation in elliptical cylindrical co-ordinates is presented in terms of the Mathieu and
modified Mathieu modal functions. This is followed by the tabulation and analysis for the
first time of the non-dimensional resonance frequencies of the transverse modes of a
rigid-wall elliptical waveguide for a complete range of aspect ratio. The modal shape patterns
of the first few circumferential radial and cross-modes are examined with particular attention
to the pressure nodal ellipses and hyperbolae. An analytical formulation is then outlined for
characterizing a single-inlet and single-outlet elliptical muffler with the inlet located on
the end face and the outlet located either on the end face or side-surface. The ensuing chapter
is devoted toward analyzing the Transmission Loss (TL) performance of different short
end-chamber mufflers namely (a) the straight-flow configuration having ports located on the
opposite face (b) the flow-reversal configuration with ports located on the same end face and
(c) configuration with inlet port on the end face and outlet on the side surface. Design
guidelines are formulated in terms of the optimal location of inlet and outlet ports which
suppresses the deteriorating influence of certain higher-order modes thereby delivering a
broadband TL performance. Directions for future work are discussed toward the end. In summary
this book is a one-stop solution for a practicing automotive engineer designing mufflers for
an applied mathematician studying wave propagation in elliptical geometries and also as a
niche area within noise control engineering.
