Spectral analysis of acoustic plane waves in ductworks with uniform and varying cross-section waveguides

The problem of low-frequency sound propagation in ducts involving varying cross-sections is analyzed. Spectral finite element formulations for the dynamic analysis of varying cross-section ducts are presented as tapered spectral elements. These elements can be used in connected waveguides through dynamic stiffness relations. Linear and polynomial duct types are considered. The elements' shape functions are established as well as the dynamic stiffness matrices describing the spectral relation between the acoustic pressure and the volume velocity. The presented spectral approach describes the acoustic wave motion at any position along arbitrary multiply connected duct waveguides within the one-dimensional plane-wave assumption. The derived expressions are verified experimentally, and by comparison with 3-D finite element solutions. The modeling of varying cross-section duct waveguides can play an important role in the design of acoustic excitation devices and horn-type loudspeakers. The advantage of the presented formulations lies in the low computational cost when compared to the finite element approach.