Sub-Bragg Phenomena in Multilayered Vibroacoustic Phononic Metamaterials

Abstract: Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve enhanced sound wave tunability in the low-frequency range in a multilayered acoustic metamaterial system. Remarkably, we reveal and study 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 simultaneously hosting two local resonances within the same bandgap. These sub-Bragg bandgaps are realized in an axisymmetric vibroacoustic phononic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The resulting coupled sound-structure interaction system is analytically solved in closed form. Furthermore, the studied multilayered vibroacoustic metamaterial exhibits sub-wavelength acoustical transparency, akin to electromagnetically induced transparency, and an acoustic analogue of low-frequency plasma oscillations, resulting in a plasma bandgap where wave propagation is entirely prohibited below the plasma frequency. These sub-wavelength phenomena, achieved predictively and well below the ubiquitous first-order Bragg diffraction range, provide broadband attenuation and superior wave manipulation capabilities for low-frequency sound. This highlights the potential of utilizing sound-structure interaction across diverse physical applications. Moreover, our findings can be extrapolated to wave propagation in broader classes of physical systems where sub-wavelength phenomena are crucial, including phononic and photonic crystals of more general configurations.