The elastodynamic giant monopole resonance of spherical void metaclusters

An isolated spherical void exhibits a strong monopolar resonance in media with Poisson’s ratio close to 1/2. For all angles of incidence, there is a single resonance peak which occurs for shear wavenumbers k_s such that k_sa ≈ 2, where a is the void radius. When a secondary void is introduced to the neighbourhood of the evacuated cavity, there are interaction effects that modify the resonance response. Here, we seek to understand the influence of multiple scattering interactions on the resonance characteristics by considering the scattering cross sections associated with a pair of resonators that are excited by a compressional field. The three-dimensional problem is modelled using a T-matrix approach in which the elastic fields are represented in a vector spherical harmonic basis. It is shown that two nearby voids are capable of producing two distinct resonances; this feature widens the range of frequencies at which resonance phenomena is observed. We derive an analytical approximation for the resonance frequency that is shown to be accurate for sufficiently soft media. We additionally consider the scattering response from a void in the presence of a soft-coated rigid particle; this configuration is shown to be capable of inducing simultaneous monopole and dipole resonances.