Elastic wave cloaking via symmetrized transformation media

Abstract

Transformation media theory, which steers waves in solids via an effective geometry induced by a refractive material (Fermat's principle of least action), provides a means of controlling vibrations and elastic waves beyond the traditional dissipative structures regime. In particular, it could be used to create an elastic wave cloak, shielding an interior region against elastic waves while simultaneously preventing scattering in the outside domain. However, as a true elastic wave cloak would generally require nonphysical materials with stiffness tensors lacking the minor symmetry (implying asymmetric stress), the utility of such an elastic wave cloak has thus far been limited. Here we develop a means of overcoming this limitation via the development of a symmetrized elastic cloak, sacrificing some of the performance of the perfect cloak for the sake of restoring the minor symmetry. We test the performance of the symmetrized elastic cloak for shielding a tunnel against seismic waves, showing that it can be used to reduce the average displacement within the tunnel by an order of magnitude (and reduce energy by two orders of magnitude) for waves above a critical frequency of the cloak. This critical frequency, which corresponds to the generation of surface waves at the cloak-interior interface, can be used to develop a simple heuristic model of the symmetrized elastic cloak's performance for a generic problem.

References in corpus (10)

• Hiding Under the Carpet: a New Strategy for Cloaking
• Achieving control of in-plane elastic waves
• Employing pre-stress to generate finite cloaks for antiplane elastic waves
• Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
• Nonlinear pre-stress for cloaking from antiplane elastic waves
• Controlling solid elastic waves with spherical cloaks
• Controlling elastic wave with isotropic transformation materials
• Control of Rayleigh-like waves in thick plate Willis metamaterials
• Scattering problems in elastodynamics
• Elastodynamic cloaking and field enhancement for soft spheres

Cited by in corpus (5)

• Nonlinear and Linear Elastodynamics Transformation Cloaking
• Transformation Cloaking in Elastic Plates
• A foliated and reversible Finsler manifold is determined by its broken scattering relation
• Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions
• Hyperelastic antiplane ground cloaking