Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates

A cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates. This is achieved through homogenization of a multiply perforated coating of isotropic homogeneous elastic material, which greatly simplifies the design of the multilayered cloak we proposed [Phys. Rev. Lett. 103, 024301 (2009)]. We first derive the homogenized biharmonic equation, which involves an anisotropic Young's modulus and an isotropic mass density. We then numerically show that a clamped obstacle is cloaked over a finite range of frequencies for an acoustic source located a couple of wavelengths away from its surrounding cloak. The reduced backward and forward scattering is confirmed by both the profile of the total field computed along a line passing through the source and the center of the cloak (near field confirmation), and the computation of the scattered far field.