In this work, without introducing mass-in-mass units or inertial amplification mechanisms, we show that two Bragg atomic chains can form an acoustic metamaterial that possesses different types of bandgaps other than Bragg ones, including local resonance and inertial amplification-like bandgaps. Specifically, by coupling masses of one monatomic chain to the same masses of a diatomic or triatomic chain, hybrid bandgaps can be generated and further be switched through the adjustment of the structural parameters. To provide a tuning guidance for the hybrid bandgaps, we derived an analytical transition parameter (p-value) for the mass-coupled monatomic/diatomic chain and analytical discriminants for the mass-coupled monatomic/triatomic chain. In our proposed mass-coupled monatomic/triatomic chain system, each set of analytical discriminants determines a hybrid bandgap state and a detailed examination reveals 14 different bandgap states. In addition to bandgap switching, the analytical p-value and discriminants can also be used as a guide for designing the coupled-chain acoustic metamaterials. The relations between the mass-coupled monatomic/triatomic chain system and a three-degree-of-freedom (DOF) inertial amplification system further indicate that the band structure of the former is equivalent to that of the latter through coupling masses by negative dynamic stiffness springs.
Erratum: Effective acoustic metamaterial homogenization based on Hamilton's principle with a multiple scales approximation [J. Acoust. Soc. Am. 147(5), 3584–3593 (2020)]
