Acoustic metamaterials (AM) have emerged as an academic discipline within the last decade. When used for sound insulation, metamaterials can show high transmission loss at low frequencies despite having low mass per unit area. This paper investigates the possibility of using AMs for increasing the sound insulation of finite single leaf walls (SLW), focusing on the coincidence effect problem. Formulas are derived using a variational technique for the forced sound transmission of finite SLW with a coupled array of single degree of freedom resonators. An analytical model is presented for this simple case, and the effects of the band gap in sound transmission and radiation are analysed. Moreover, the influence of each parameter is studied giving way to an optimized way of designing this type of structures using constrained parameter optimization. Different objective functions are compared and discussed. Finally, some conclusions are drawn regarding the effectiveness of the proposed model, possible applications, and future work.

Acoustic metamaterials are becoming promising solutions for many industry applications, but the gap between theory and practice is still difficult to close. This research proposes an optimization methodology of acoustic metamaterial designs for sound insulation that aims to start bridging this gap. The proposed methodology takes advantage of a hybrid analytical-numerical approach for computing the sound transmission loss of the designs efficiently. As a result, the implementation of optimization techniques on numerical model designs becomes practically possible. This is exemplified with two test cases: (i) optimization of the sound transmission loss of a single gypsum board panel and (ii) optimization of the noise reduction of outdoor HVAC units. Two resonator designs, one used previously for sound radiation in flat panel speakers and the other for enhancing the sound transmission loss at the mass-air-mass resonance of double panels, are here optimized for the two test cases. This shows how an existing resonator can be adapted for new purposes, thus making the design of acoustic metamaterials efficient. The optimized metamaterials outperform the original designs as well as traditional approaches to sound insulation.