Acoustic metamaterial elements from tunable elastic shells

Abstract

Elastic shells are used as elements in novel acoustic metamaterials. Tuning the shells produces unnatural and favorable acoustic qualities in the quasi-static regime. This is achieved by internally stiffening the shell with an axisymmetric distribution of springs which connect the added central mass to the shell. The two parameters: stiffness and mass are carefully optimized for the desired effect. Flexural resonances of the shell dominate the frequency response, but are constrained in the quasi-static regime as shown by the analytical model. As an example of transparency, an aluminum shell of radius 1 cm is tuned to water with and acrylic internal oscillator exhibiting a near-zero scattering cross section up to ka = 0.6. Also, individually tuning each shell in a fluid saturated array is a means of creating devices based on transformation acoustics such as a cylindrical to plane wave lens. Investigations of favorable high frequency effects and active tuning are presented. Another method of changing the effective acoustic properties of a shell is to attach a second shell to the inside creating a composite structure. The thickness of each shell is optimized to yield desired effective medium properties. Tuning to water yields a broad frequency range of transparency.