Design of continuously graded elastic acoustic cloaks

Abstract

This letter demonstrates the design of continuously graded elastic cylinders to achieve passive cloaking from harmonic acoustic excitation, both at single frequencies and over extended bandwidths. The constitutive parameters in a multilayered, constant-density cylinder are selected in a partial differential equation-constrained optimization problem, such that the residual between the pressure field from an unobstructed spreading wave in a fluid and the pressure field produced by the cylindrical inclusion is minimized. The radial variation in bulk modulus appears fundamental to the cloaking behavior, while the shear modulus distribution plays a secondary role. Such structures could be realized with functionally-graded elastic materials.