Multimodal resonant metamaterials for broadband sound transmission loss improvement

Locally resonant metamaterials (LRMs) are a promising approach for enhancing the vibroacoustic attenuation of partitions. LRMs originate when adding small resonators on the microscale (sub-wavelength scale) to a host structure for targeting exceptional material properties on the macro-scale. While conventional LRMs exploit single-mode translational resonators resulting in narrowband attenuation, the potential for broader attenuation offered by resonators with multiple translational and rotational modes has been recently demonstrated through numerical simulation. However, their effectiveness has not yet been experimentally demonstrated, and the optimized design of multi-modal resonators for broadband attenuation is highly nontrivial. This work focuses on both aspects. First, a multimodal rotational LRM for a cross-laminated timber host structure and medium-density fiberboard resonators is designed and manufactured. A subsequent transmission loss test reveals the effective suppression of the broad coincidence transmission loss dip of the orthotropic host panel through two resonance peaks. Next, a methodology for optimized resonator design is developed. The optimization objective is to maximize the broadband diffuse transmission loss while constraining mass. The topology optimization problem is solved by gradient-based mathematical programming, for which the necessary (adjoint) sensitivities of objectives and constraints are derived. The efficacy of this approach is demonstrated through detailed numerical simulation.