Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Abstract

Given the flexibility of choosing negative elastic parameters, we construct material structures that can induce two resonance phenomena, referred to as the elastodynamical resonances. They mimic the emerging plasmon/polariton resonance and anomalous localized resonance in optics for subwavelength particles. However, we study the peculiar resonance phenomena for linear elasticity beyond the subwavelength regime. It is shown that the resonance behaviors possess distinct characters, with some similar to the subwavelength resonances, but some sharply different due to the frequency effect. It is particularly noted that we construct a core–shell material structure that can induce anomalous localized resonance as well as cloaking phenomena beyond the quasistatic limit. The study is boiled down to analyzing the so‐called elastic Neumann–Poincaré (N‐P) operator in the frequency regime. We provide an in‐depth analysis of the spectral properties of the N‐P operator on a circular domain beyond the quasistatic approximation, and these results are of independent interest to the spectral theory of layer potential operators.

An optimization method for the inverse scattering problem of the biharmonic wave

“…Introduction. The inverse scattering problems to determine the obstacle/scatterer from the time-harmonic acoustic, elastic, or electromagnetic waves have received mounting attention due to their wide applications in nondestructive testing, bio-medical imaging, underwater object identification, and many other scenarios [4,7,14,18]. In contrast, the inverse cavity scattering problems in an infinitely thin elastic plate, which is governed by the biharmonic wave equation, is much less investigated.…”