Design of Continuously Graded Acoustic Cloaks

Clay Sanders, Duke University

A methodology is presented for the design of continuously graded elastic cylinders to achieve passive cloaking from harmonic acoustic excitation, both at single frequencies and over extended bandwidths. Efforts to design acoustic cloaks, based on transformation acoustics, typically rely on distributions of anisotropic material to achieve cloaking. We investigate the design of a graded composite structure featuring isotropic elastic materials that can achieve similar cloaking behavior. 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 harmonic spreading wave in a fluid and the pressure field produced by the cylindrical inclusion is minimized. A quasi-Newton method, using adjoint-based gradient calculations, is used to solve the optimization problem. The radial variation in bulk modulus appears fundamental to the cloaking behavior, while the shear modulus distribution plays a secondary role. Designs are unique to excitation frequency, but do achieve cloaking behavior over extended frequencies. Such structures could be realized with novel, functionally graded elastic materials.

Abstract Author(s): Clay Sanders, Wilkins Aquino, Timothy Walsh