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 of the body- and face-centered cubic lattice systems encompassing nodal isotropic multivibrators are investigated. Our main results are: (1) number bandgaps equals number, n, internal masses as each is a result classical analog quantum level-repulsion mechanism between external oscillations, (2) upper boundary frequencies, ωupper2i, i = 1, 2, ⋯, gaps formed coincide with eigen-frequencies, ωint;i2 ≠ 0, isolated multivibrator, ωupper2;i ωint; i2, lower ωlower2,i2, good agreement estimations ωlower,i2≈ω^int;i2 (ωlower,i2<ω^int;i2), where ω^int;i2 represent eigen-frequencies multivibrator when its shell motionless. The morphologies set dispersion surfaces, ωm2(k), m …, 6, corresponding passbands similar to other that ωext; m2(k), obtained through exclusion masses. Thus, problem analyzing acoustic properties complicated system reduced study two simple sets {ωint; i2} ω^int;i2, along {ωext; m2(k)}, morphology which depends only on type symmetry. This splitting renders controlled formation homogeneous feasible.