A set of periodic rigid inclusions are embedded in a porous lining to enhance the sound attenuation in an acoustic duct at low frequencies. Floquet-Bloch theorem is introduced to investigate the sound attenuation in a 2D infinite waveguide lined with periodic inclusions embedded in porous material. Crossing is observed between the mode attenuations of two Bloch waves. Here the mode coupling is due to the presence of the inclusions embedded in the porous material. The most important and interesting figure is that near the frequency where the crossing of the mode attenuations appears, an attenuation peak is observed. This phenomenon can be used to explain the transmission loss peak observed numerically and experimentally in a 3D waveguide with a finite portion of its wall lined by a porous material embedded with periodic inclusions.
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