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 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.