More frequently, recent low-frequency noise control techniques commonly implemented in aerospace and ground transportation as well as in building applications are based on acoustic metamaterial concepts. The technologies proposed in the literature, using layered porous materials with embedded Helmholtz resonators (HR), exhibited considerable potential when tuned at tonal, multi-tonal or narrow frequency bands. Our recent investigations have shown that the acoustical performance of these metamaterials can be further improved by the use of resonators with complex shaped necks. These necks can be designed and optimized to minimize the HR resonance frequencies (small form factor) and maximize the sound transmission loss (STL) performance.
This paper presents the developed design optimization method for HRs with complex neck shapes recessed within the HR cavity. The HRs were embedded in a layer of porous material. The implemented approach was based on the transfer matrix methods (TMM) in series and in parallel coupled to a multi-objective optimization. Complex optimum neck shapes were obtained allowing for a shift towards the low frequencies of the resonator resonance with a good STL performance. Moreover the STL calculated using the TMM approach were observed to be in excellent agreement with the finite element method numerical results.