Multi-resonator metamaterials as multi-band metastructures

Abstract

Introducing multi-resonator microstructure into phononic metamaterials provides more flexibility in bandgap manipulation. In this work, 3D-acoustic metamaterials of the body- and face-centered cubic lattice systems encompassing nodal isotropic multivibrators are investigated. Our main results are: (1) the number of bandgaps equals the number, n, of internal masses as each bandgap is a result of the classical analog of the quantum level-repulsion mechanism between internal and external oscillations, and (2) the upper boundary frequencies, ωupper 2 i , i = 1, 2, ⋯, n, of the gaps formed coincide with eigen-frequencies, ωint;i 2 ≠ 0, of the isolated multivibrator, ωupper2 ;i= ωint; i 2 , and the lower boundary frequencies, ωlower 2, i 2 , are in good agreement with estimations as ω2 lower,i ≈ωb 2 int;i (ω2 lower,i <ωb 2 int;i), where ωb 2 int;i represent the eigen-frequencies of the multivibrator when its external shell is motionless. The morphologies of the set of dispersion surfaces, ωm 2 (k), m = 1, 2, …, 6, in the corresponding passbands are similar to each other and to that of the set of dispersion surfaces, ωext; m 2 (k), obtained through the exclusion of internal masses. Thus, the problem of analyzing the acoustic properties of the complicated system is reduced to the study of two simple sets {ωint; i 2 } and ωb 2 int;i n o, along with {ωext; m 2 (k)}, the morphology of which depends only on the type of lattice symmetry. This splitting renders controlled phononic bandgaps formation in homogeneous multi-resonator metamaterials feasible.