Achieving Control of In-plane Elastic Waves

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. Recently, significant progress has been made on the control of acoustic and electromagnetic waves. Transformation based solutions to the conductivity and Maxwell’s equations in curvilinear coordinate systems, subsequently reported by Greenleaf et al. [1] and then by Pendry et al. [2] and Leonhardt [3], enable one to bend electromagnetic waves around arbitrarily sized