Rotational and multimodal local resonators for broadband sound insulation of orthotropic metamaterial plates

Locally resonant metamaterials are employed to increase the sound insulation of a host structure. In orthotropic host structures, the direction-dependent bending stiffness leads to a broad coincidence dip in sound transmission loss, which is difficult to overcome through conventional metamaterial solutions based on single-mode translational resonators. For this reason, in this paper we aim at developing orthotropic metamaterials with rotational resonators, exhibiting a direction-dependent effectiveness, and with multimodal resonators, which combine translational and rotational modes and are effective in a broader frequency band. First, we develop an analytical effective medium model of sound transmission in multimodal orthotropic metamaterials, which exhibit similar accuracy to simulations exploiting a wave and finite element method. We then propose a design methodology for realizable geometrical layouts of multimodal resonators, by exploiting numerical optimization to maximize the broadband sound transmission loss of the metamaterial. For two selected design cases, we show that rotational and multimodal metamaterials can suppress the broad coincidence dip of orthotropic plates, when the frequencies of local resonances are tuned within the coincidence region. The results of the work open up new possibilities for broadband sound insulation through metamaterial solutions.