For a spherical elastic inclusion, the paper gives explicit finite-frequency eigenvalues and eigenfunctions of the Neumann-Poincaré operator and constructs core-shell metamaterials whose anomalous resonances cloak sources inside a critical radius.
Cloaking by anomalous localized resonance for linear elasticity on a coated structure
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abstract
We investigate anomalous localized resonance on the circular coated structure and cloaking related to it in the context of elasto-static systems. The structure consists of the circular core with constant Lam\'e parameters and the circular shell of negative Lam\'e parameters proportional to those of the core. We show that the eigenvalues of the Neumann-Poincar\'e operator corresponding to the structure converges to certain non-zero numbers determined by Lam\'e parameters and derive precise asymptotics of the convergence. We then show with estimates that cloaking by anomalous localized resonance takes place if and only if the dipole type source lies inside critical radii determined by the radii of the core and the shell.
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math.AP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limit
For a spherical elastic inclusion, the paper gives explicit finite-frequency eigenvalues and eigenfunctions of the Neumann-Poincaré operator and constructs core-shell metamaterials whose anomalous resonances cloak sources inside a critical radius.