Study of Two-Dimensional Acoustic Metamaterial Based on Lattice System

This article presents a comprehensive study of two-dimensional acoustic metamaterial based on mass-in-mass lattice model with both one resonator and multi-resonators. We demonstrate the dynamic anisotropic property of a two-dimensional lattice system and the existence of multiple stop bands of mass-in-mass lattice systems with more than one resonator. A two-dimensional stable lattice plate structure, composed of unit mass-in-mass cells is proposed, and been studied by adapting both an exact model and a continuum model. The dispersion surfaces and stop band obtained by the exact model show that the stop band of this metamaterial exists, and it can be shifted and operated upon. In contrast, the dispersion surface obtained through the continuum model describes the acoustic mode well, but is only accurate at low frequencies for the optical mode. By attaching a secondary resonator to the primary resonator, an additional stop band is achieved. Finally, an acoustic metamaterial plate which has more than one stop band is proposed and studied numerically. Good agreement has been achieved between theoretical and numerical analyses.