Multi-resonator metamaterials as multi-band metastructures

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, omega(2i)(upper), i = 1, 2, ..., n, of the gaps formed coincide with eigen-frequencies, omega(2)(int;i) not equal 0, of the isolated multivibrator, omega(upper2;i) = omega(2)(int; i), and the lower boundary frequencies, omega(2)(lower2,i), are in good agreement with estimations as omega(2)(lower;i)approximate to(omega) over cap (2)(int;i) (omega(2)(lower;i) < <(omega)over cap>(2)(int;i)), where (omega) over cap (2)(int;i) represent the eigen-frequencies of the multivibrator when its external shell is motionless. The morphologies of the set of dispersion surfaces, omega(2)(m)(k), m = 1, 2, ..., 6, in the corresponding passbands are similar to each other and to that of the set of dispersion surfaces, omega(2)(ext; m)(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 {omega(2)(int; i)} and {(omega) over cap (2)(int;i)}, along with {omega(2)(ext; m)(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. (C) 2021 The Author(s). Published by Elsevier Ltd.