Ventilated Hexagonal acoustic Metamaterial plate based on sided branches Helmholtz resonators with multiple local resonances

The development and application of noise control strategies on subwavelength regimes have thus demanded a continuous effort by several researchers. In this context, the advent of acoustic metamaterials arose as a novel strategy for the manipulation and control of sound waves of subwavelength dimensions and the development of lightweight acoustic devices. Previously research has evidenced the capacity of symmetric-axially acoustic systems to achieve impressive acoustical absorption behaviours in broadband, enabled by the critical coupling of resonators with distinct resonances. Here, we further extend the idea of an acoustic metamaterial plate conceptualized to manipulate the front wave propagation and sound attenuation characteristics in a ventilated acoustic system comprising multiple subwavelength resonators in the form of a panel, herein named Acoustic Hexagonal Metamaterial (AHM), consequently, the high capacity to handle the sound transmission loss (STL) is theoretically (using dissipative fluid equivalent approach) and numerically (using boundary layer impedance method) reported. Thus, AHM is realized by expanding the theory of in-parallel coupling of tunned Helmholtz Resonators under grazing incidence into each unit cell section. The respective attenuation mechanism results from the compressive extensional movement, conducting to a negative effective bulk modulus value, therefore a bandgap is generated, shown by the respective dispersion curves, herein theorized as single, dual, and triple resonance, resulting from the organization of group and sets of Helmholtz resonators. Based on this, we initially demonstrate numerically and analytically the averaged transmission 20 dB around the audible range at approximately 800Hz until 3kHz, and achieving specific gaps around 50 dB at tunned frequencies. The obtained results are promising and expand the applicability of these axially symmetric devices in the development of novel compact attenuators with applications in different engineering contexts, especially in building environments.