## Abstract

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.

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.

Original language | English |
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Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Publication status | Published - 2022 |