Defects in a periodic structure formed by two different side-branches grafted in series

Abstract

We present an original examination of the sound transmission in a periodic structure with two different
side-branches grafted in series. These branches have different boundary conditions at their extremities.
One of them is a closed side-branch, while the other has an open termination. The resonators and the main
waveguide tubes, where the resonators are grafted in, are filled with the air. This theoretical research
reveals that the combination of a high-pass filter and a low-pass filter can function effectively as a highfrequency wave reflector. Which can be used in noise reduction. When defective resonators replace
segments of a rigid or open termination, localized modes appear inside the bandgaps. The numerical results
show that the transmission of localised modes is very sensitive to the cross-section of the defective
resonators. The calculations of the transmission have done using the Transfer Matrix Method. The
proposed structure can be used as an acoustical filter.