Low-frequency sub-Bragg phenomena in multilayered vibroacoustic metamaterials

Abstract

Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve broadband low-frequency sound manipulation at the sub-wavelength scale in a multilayered vibroacoustic metamaterial. Remarkably, we unveil the formation of genuinely sub-wavelength Bragg-like band-splitting induced bandgaps, generalizing the "band-folding induced bandgaps" in the literature. Additionally, we propose a methodology to widen sub-wavelength local resonance bandgaps by hosting two local resonances within the same bandgap. These sub-Bragg phenomena are realized at low frequencies in an axisymmetric vibroacoustic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The coupled sound-structure interaction is solved exactly. The studied system exhibits sub-wavelength acoustical transparency, akin to “electromagnetically induced transparency”, and an acoustic analogue of "plasma oscillations". We derive canonical conditions for the emergence of band-splitting bandgaps, showing they are exclusive to multilayered configurations. These band-splitting bandgaps resemble Bragg bandgaps in their attenuation, band-crossing capabilities, and potential to host topological interface states. We also reveal that classical geometric Bragg diffraction does not apply to the periodic multilayered vibroacoustic configurations examined. The studied sub-wavelength phenomena unlock new possibilities for controlling low-frequency wave propagation in the sub-Bragg regime. Design guidelines for maximizing bandgap width within the low-frequency regime are provided, and the attenuation performance across different bandgaps is demonstrated through numerical simulations. We anticipate that our findings, while demonstrated here in vibroacoustic metamaterials, provide a promising approach for advanced acoustic devices, and could inspire future work exploring similar sub-wavelength mechanisms in other classes of physical systems.