Directional cloaking of flexural waves in a plate with a locally resonant metamaterial.
This paper deals with the numerical design of a directional invisibility cloak for backward scattered elastic waves propagating in a thin plate (A0 Lamb waves). The directional cloak is based on a set of resonating beams that are attached perpendicular to the plate and are arranged at a sub-wavelength scale in ten concentric rings. The exotic effective properties of this locally resonant metamaterial ensure coexistence of bandgaps and directional cloaking for certain beam configurations over a large frequency band. The best directional cloaking was obtained when the resonators' length decreases from the central to the outermost ring. In this case, flexural waves experience a vanishing index of refraction when they cross the outer layers, leading to a frequency bandgap that protects the central part of the cloak. Numerical simulation shows that there is no back-scattering in these configurations. These results might have applications in the design of seismic-wave protection devices.
ISTerre Université Joseph Fourier, Grenoble, BP 53 38041 Grenoble Cedex 9, France.
Andrea
A
Colombi
ISTerre Université Joseph Fourier, Grenoble, BP 53 38041 Grenoble Cedex 9, France.
Philippe
P
Roux
Institut Fresnel-CNRS, Unité Mixte de Recherche 7249, Aix-Marseille Université, 13397 Marseille Cedex 20, France.
Sebastien
S
Guenneau
Institut Langevin, ESPCI ParisTech-CNRS, Unité Mixte de Recherche 7587, 1 Rue Jussieu, 75005, Paris, France.
Matthieu
M
Rupin