Dispersion transitions and pole-zero characteristics of finite inertially amplified acoustic metamaterials

摘要

This work presents a comprehensive analysis of wave dispersion patterns and band gap formation associated with Inertially Amplified Acoustic Metamaterials (IAAM). The findings explain the different mechanisms by which inertial amplification affect wave dispersion in the individual IAAM cell as well as the evolution of such effects in finite configurations of these cells. Derived expressions for acoustic wave dispersion in IAAMs reveal unique features including flat dispersion branches with zero group velocity and a transition from a metamaterial (local resonance) to a phononic behavior that is directly related to the location and magnitude of the inerter elements. Using a closed-form transfer function approach, the translation of such effects to IAAM realizations with a known number of cells is interpreted from the pole-zero distributions of the resultant finite structures. It is also shown that band gaps are not always necessarily enlarged in the presence of inertial amplification. Comparing with benchmark conventional acoustic metamaterials, the conditions leading up to favorable as well as inferior IAAM designs are fully derived. Finally, an alternative resonator-free acoustic metamaterial is presented and shown to exhibit local resonance effects under appropriately tuned conditions. Published by AIP Publishing.