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Sound attenuation analysis and optimal design for a duct with periodic membranes embedded in its sidewalls

Ducts with membranes in their sidewalls have been used for noise control due to their remarkable ability to reflect sound waves at low frequencies. To obtain a broader attenuation band, combining several membranes is one possible way, which leads to yet another branch of engineering called phononic crystals or acoustic metamaterials. This study analyzes sound wave propagation and attenuation in a duct with periodic membranes embedded in its sidewalls. For each cell, an analytical, fully coupled vibro-acoustic model is proposed via energy formulation, and then the interference among multiple membrane cells is treated using the cell transfer matrix. Our study provides an efficient means to predict, and eventually optimize, the acoustic bandgap structure. Results from the current model fit well with those simulated using a two/three-dimensional finite element method. The 2D membrane with free lateral edges was found to perform almost as well as its 1D counterpart. Moreover, a better bandgap can be achieved via coupling of resonance and Bragg reflection. The effects of periodic distance and membrane tension force on the bandgap structure are then discussed and analyzed to determine their appropriate parameters. Some optimal designs are implemented through artificial disorder, which shows promising potential in attenuating bandwidth expansion compared with the original periodic configuration.Ducts with membranes in their sidewalls have been used for noise control due to their remarkable ability to reflect sound waves at low frequencies. To obtain a broader attenuation band, combining several membranes is one possible way, which leads to yet another branch of engineering called phononic crystals or acoustic metamaterials. This study analyzes sound wave propagation and attenuation in a duct with periodic membranes embedded in its sidewalls. For each cell, an analytical, fully coupled vibro-acoustic model is proposed via energy formulation, and then the interference among multiple membrane cells is treated using the cell transfer matrix. Our study provides an efficient means to predict, and eventually optimize, the acoustic bandgap structure. Results from the current model fit well with those simulated using a two/three-dimensional finite element method. The 2D membrane with free lateral edges was found to perform almost as well as its 1D counterpart. Moreover, a better bandgap can be achieved v...