An analytical model for broadband sound transmission loss of a finite single leaf wall using a metamaterial

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 to increase the sound insulation of finite single leaf walls (SLWs), focusing on the coincidence effect problem. Formulas are derived using a variational technique for the forced sound transmission of finite SLWs 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 analyzed. Moreover, the influence of each parameter is studied, especially the presence of losses, giving way to an optimized way of designing this type of structure using constrained parameter optimization. Numerical validations are performed and discussed. Finally, some conclusions are drawn regarding the effectiveness of the proposed model, including possible applications.