An effective medium model for sound insulation analysis of (in)finite multi-modal vibroacoustic metamaterials

Vibroacoustic metamaterials are used to improve the sound insulation of a host panel by periodically attaching local resonators.While most vibroacoustic metamaterials exploit single-mode resonators for narrowband improvements, the use of multi-modal resonators has recently emerged to extend the frequency band of effectiveness.However, significant modelling and computational challenges need to be tackled when designing adequate resonator layouts that exploit multiple modes to influence broadband sound transmission.In this work, we show that analytical effective medium models can accurately predict the performance of vibroacoustic metamaterials, simply requiring the extraction of modal parameters from the analysis of the fixed-based resonator.Effective medium models are used to analyze diffuse field sound transmission loss both for infinite structure dimensions, through analytical formulas, and for finite size, through combination with the hybrid deterministic -Statistical Energy Analysis.The accuracy of the proposed prediction methodologies is validated for two different multi-modal metamaterial layouts, that target the suppression of the broadband insulation dip due to coincidence in orthotropic host panels.