Analytical study by transfer matrix and Green's method of a periodic lattice formed by dual Helmholtz resonators (DHR)

Abstract

The subject of this paper is to study a periodic structure composed of a number of identical structural components that are joined together end-to-end and/or side-byside to form a whole complex. Each elementary cell is formed by double Helmholtz Resonators. We know that the Helmholtz resonators are often used to reduce noise and they are particularly useful when noise has a narrow frequency band. In this study we aim to exanimate the effect of combining many resonators. Double or dual resonators have been studied by two analytical methods: transfer matrix and Green function method. The last method (Green's method) called also the interface response method used in the beginning on material sciences for modeling photonics and phononics problems. The present work therefore concentrates on the acoustic characteristics including both the dispersion relation and the transmission loss of double Helmholtz resonators. The objective is to investigate the acoustic attenuation performance of dual Helmholtz resonators by developing original analytical expressions.