The effect of inertial distribution on dispersive modes in pentamode metamaterials for use in acoustic cloaking

Abstract

Transformation acoustics uses invertible maps to transform a cloaked region to a region with a smaller scatterer. The “elastic” or Norris class of acoustic cloaking theory is inherently broadband, in that it does not rely on the presence of resonant effects. To achieve the properties required by the transformation theory, we utilize pentamode materials, which admit the use of finite mass but require anisotropic stiffness throughout the material. These types of materials do not exist naturally and must be fabricated through the use of metamaterials. One of the challenges associated with metamaterials for use in dynamic applications is the distribution of mass in a unit cell and its consequences for frequency-dependent behavior in the metamaterial. Various homogenization techniques for recovering wave speed properties of the metamaterial unit cells may predict contradictory wave speed values for pentamodal structures. These disagreements can be explained through the distribution of inertia in the material and the resulting proliferation of dispersive modes present in the Bloch-Floquet diagrams. This effect will be described within the context of static homogenization, Bloch-Floquet theory, and numerical experiments effected through finite element software PZFlex. An approach for optimization of these metamaterials with respect to the dispersive modes will be discussed.