Prediction of the sound transmission loss of shape-varied sonic crystals: A transfer matrix approach

This paper proposes a transfer matrix method (TMM) for modeling sonic crystals to predict the transmission loss of noise exiting an air extraction system. Because the crystals may be of different shapes (e.g., square, circular, or standardized airfoil profile to minimize airflow resistance) and must account for thermo-viscous losses, a discrete version of the TMM is used. Similar to the finite element method, a discretization of the geometry is first performed. Each element is modeled with a transfer matrix (TM) that includes the local thermo-viscous losses which attenuate the sound wave. For each element in parallel, the parallel TMM is employed. For the subsequently created elements in series, the classic TMM is used. This generates a global TM from which the sound transmission loss of the crystal network is deduced. The predictions obtained by the proposed method are compared to measurements in an acoustic tube for three different shapes of sonic crystals. The results show that a geometric tortuosity correction is necessary for the predicted bandgap center frequency to match the measurement. A correction is proposed, but this requires a possible refinement for more complicated profiles.