The use of a serial system of cylindrical and concentric Helmholtz resonators for Low Frequency Sound Absorption Alexander DELL (1) , Anton KRYNKIN (2) (1) University of Sheffield, United Kingdom, AJDell1@Sheffield.ac.uk (2) University of Sheffield, United Kingdom, a.krynkin@sheffield.ac.uk 01/06/2018 Abstract A theoretical and numerical study of sound propagation in a serial system of cylindrical and concentric Helmholtz resonators is conducted. By altering the geometry of each subsequent Helmholtz resonator it is possible to gen- erate very low frequency resonances. Using the transfer matrix method an analytical formulation for the acoustic absorptive properties of the this serial configuration is proposed. An optimization method is developed to tune the system for the absorption of sound waves at specific frequency ranges. Through this study it is shown that using an optimized configuration of Helmholtz resonators in the low frequency range, sound absorption can be achieved at sub-wavelength sample thicknesses. The results of the analytical study are validated through numerical means. Keywords: Helmholtz resonator, Absorption, Optimisation 1 INTRODUCTION Typically used sound absorbers consist of bulky porous/ fibrous materials which is often impractical for low frequency sound absorption due to the mass-density law [2]. To overcome this, acoustic metamaterials con- sisting of Helmholtz resonators are have been utilised to achieve broadband sound absorption at sub-wavelength thicknesses [3]. Of particular relevance to this paper is the extensive research that has been undertaken on cylin- drical and concentric Helmholtz resonators using the Transfer Matrix Method (TMM) [5, 9, 7, 6], highlighting how this relatively simple analytical method can be a useful tool for the analysis and optimisation of various configurations of Helmholtz resonators. This report sets out a theoretical model to analyse the absorption characteristics for a serial system of N cylin- drical, concentric Helmholtz resonators, extending the work conducted on duel resonators in [10]. This also provides a simple and computationally inexpensive method in which optimisation can then be implemented to maximise the absorption at desired frequencies. A comparison is then made between the results obtained an- alytically and those produced by numerical analysis for validation. This is done for the case of three serial Helmholtz resonators. 2 GEOMETRY An axisymmetric view of the studied geometry can be seen in figure 1. Here it is evidenced that the geometry consists of a waveguide in which the end is loaded with a serial system of Helmholtz resonators. These are placed end-to-end and the Nth resonator cavity results in velocity termination. The plane wave propagates from left to right. It is worth noting that Rt denotes the radius of the waveguide, Rn i denotes the neck radius for the ith HR and Rc i denotes the cavity radius for the ith HR. Ln i and Lc i denote the length of the neck and cavity for the ith HR, respectively. 4480