Deeply subwavelength giant monopole elastodynamic metacluster resonators

The Giant Monopole Resonance is a well-known
phenomenon, employed to tune the dynamic response
of composite materials comprising voids in an elastic
matrix which has a bulk modulus much greater than
its shear modulus, e.g. elastomers. This low-frequency
resonance (e.g. λp/a ≈100 for standard elastomers,
where λp and a are the compressional wavelength
and void radius respectively) has motivated acoustic
material design over many decades, exploiting the
subwavelength regime. Despite this widespread
use, the manner by which the resonance arising
from voids in close proximity is affected by their
interaction is not understood. Here we illustrate
that for planar elastodynamics (circular cylindrical
voids), coupling due to near-field shear significantly
modifies the monopole (compressional) resonant
response. We show that by modifying the number
and configuration of voids in a metacluster, the
directionality, scattering amplitude and resonant
frequency can be tailored and tuned. Perhaps most
notably, metaclusters deliver a lower frequency
resonance than a single void. For example, two
touching voids deliver a reduction in resonant
frequency of almost 16% compared with a single void
of the same volume. Combined with other resonators,
such metaclusters can be used as meta-atoms in
the design of elastic materials with exotic dynamic
material properties.