Achieving control of in-plane elastic waves

TL;DR

This paper derives the elastic properties of a cylindrical cloak capable of controlling in-plane elastic waves, demonstrating its effectiveness through numerical simulations that show cloaking of obstacles regardless of wave frequency or polarization.

Contribution

It introduces a novel elastic cloak with a rank 4 tensor derived from geometric transform, maintaining Navier equations' form, and verifies cloaking via numerical analysis.

Findings

Cloak effectively hides obstacles from elastic waves

Cloaking works across different frequencies and polarizations

Elastic properties derived from geometric transform

Abstract

We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [Milton et al., New J. Phys. 8, 248 (2006)]. We numerically check that clamped and freely vibrating obstacles located inside the neutral region are cloaked disrespectful of the frequency and the polarization of an incoming elastic wave.