Bliss D., Danilov P., Burton L., Nesbitt J.

Sound propagation of quasi one-dimensional waves through a duct with spatially periodic area changes has been studied theoretically and experimentally. The resulting wave behavior is similar to that observed for periodic structures, with Bloch waves, and pass-bands and stop-bands. This configuration substantially reduces sound transmission from noise sources having harmonics that fall in the stop bands, while having little effect in pass bands. The present study adapts this concept to configurations with dissipative sound absorbing material. The periodically spaced regions of the duct with larger cross-sectional area are partially filled with porous material, so that the open cross-sectional area remains constant throughout the duct. The duct is analyzed as a quasi one-dimensional system using an approach based on periodic structure theory. An approach based on transfer matrix properties across each spatial period section facilitates the derivation of the overall behavior. The porous material makes the propagation wavenumber in the porous/open subsections complex, thereby changing the nature of the stop and pass bands in the overall system, and providing significant attenuation even in pass bands. A fairly simple theory to predict the complex wavenumber is developed and experimentally verified. Results demonstrate that the best attenuation strategy may be to distribute the porous material in periodically spaced sub-regions rather than in either a single larger volume, or in a uniform distribution all along the duct, particularly if cancellation of discrete harmonics is desirable. Theoretical predictions and experimental results are presented and compared.