On the Hybrid Modelling of Rigid Sonic Crystal Embedded in Plenum Chamber at Low Frequencies Using the Effective Medium Approach and Finite Element Method

Abstract

This study explores the application of homogenization schemes in modelling acoustic wave propagation in a finite array of circular scatterers embedded into a 2D cavity. The cavity is integrated into the 2D waveguide attached to the cavity inlet and outlet. Square-lattice sonic crystal (SC), composed of rigid and radially symmetric circular cylinders, is used to represent the finite array in this study. The model is aimed at informing the novel designs of plenum windows with superior soundproofing performance. The sound transmission performance is analysed with hybrid numerical simulation using the Finite Element Method (FEM) and homogenization scheme. A theoretical homogenization method based on the Effective Medium Approach (EMA) is reviewed and implemented on the modelling of the SC array inside the cavity at low frequencies and then implemented in FEM. Comparison of the transmission loss (TL) reveals a high degree of matching between settings with and without homogenization at low-frequency range. It is observed that performance of the hybrid model maintains a high degree of matching provided the cavity modes are dominated by a single characteristic scale in the low frequency. This includes the case of a narrow plenum chamber with only a single cylinder placed inside the cavity with a width of one lattice constant. This homogenization method is proven to be more computationally efficient in FEM compared to the modelling of exact geometry of the problem.