Optimized reactive silencers composed of closely-spaced elongated side-branch resonators

This paper reports a theoretical study of the sound propagation in a rectangular waveguide loaded by closely-spaced elongated side-branch resonators forming a simple low-frequency broadband reactive silencer. Semi-analytical calculations account for the evanescent modes both in the main waveguide and side-branch resonators and for the viscothermal losses in the silencer elements. Reasonable accuracy is maintained in the evaluation of transmission, reflection, and absorption coefficients, while the calculation time is reduced by a few hundred times in comparison with the finite element method. Therefore, the proposed method is particularly suitable for optimization procedure. The lengths of the individual equally spaced side-branch resonators are optimized by a heuristic evolutionary algorithm that maximizes the minimum transmission loss (TL) over a pre-defined frequency range. Numerical results indicate that the minimum TL of the optimized silencers is reduced due to the destructive effect of the evanescent coupling from the resonators of the nearest side-branches. In the opposite, the TL increases linearly with the number of the side-branch resonators.