Transmission Loss Analysis of a Parallel-Coupled Helmholtz Resonator Network with a Green's Function Approach

To reduce the transmission of multiple tones or broadband noise, Helmholtz resonators with a narrow frequency bandwidth are typically used in aircraft cabins. However, the space available for applying such resonators is limited. To effectively use the space and to increase transmission loss (TL), a parallel-coupled Helmholtz resonator network, with two resonators connected via a thin compliant membrane, was designed and experimentally tested. It was found that the compliant membrane motion plays an important role in the production of additional TL peaks. A numerical model of a parallel-coupled resonator network was then developed to simulate the experiments. The rate of cavities volume change due to the presence of the compliant membrane is described in detail with the aid of the appropriate motion equation of the membrane by using Green’s function approach. Good agreement between the numerical and experimental results is found. Furthermore, insight into the effect of membrane mechanical properties on the production of TL peaks was provided by the numerical model. Finally, to broaden the effective frequency range of the resonator network, the membrane vibration is actively controlled by implementing a trust-region Newton conjugate-gradient method. Transmission loss is found to increase to approximately 25 dB over a broad frequency range.