Cloaking in-plane elastic waves with swiss rolls

Abstract

We propose a design of cylindrical elastic cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as swiss-rolls. The scaling factor between inclusions' sizes is according to Pendry's transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields $\mathbf{u}$ in original medium and ${\mathbf{u}}^{\prime }$ in transformed medium remain unaffected (${\mathbf{u}}^{\prime }=\mathbf{u}$), and this breaks the minor-symmetries of the rank-4 and rank-3 tensors in the Willis equation that describes the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located near a clamped obstacle surrounded by the structured cloak. Such an effective medium allows for strong Willis coupling [Quan et al., Physical Review Letters {\bf 120}(25), 254301 (2018)], notwithstanding potential chiral elastic effects [Frenzel et al., Science {\bf 358}(6366), 1072 (2017)], and thus mitigates roles of Willis and Cosserat media in the achieved elastodynamic cloaking.

arXiv comment7 pages, 3 figures

References in corpus (7)

• Achieving control of in-plane elastic waves
• Maximum Willis Coupling in Acoustic Scatterers
• An asymmetric elastic metamaterial model for elastic wave cloaking
• Acoustic meta-atom with maximum Willis coupling
• Controlling solid elastic waves with spherical cloaks
• On static chiral Milton-Briane-Willis continuum mechanics
• Steering in-plane shear waves with inertial resonators in platonic crystals

Cited by in corpus (3)

• Cloaking strategy for Love waves
• Dynamic cloaking of a diamond-shaped hole in elastic plate
• Mechanically concealed holes