Tunable acoustic metamaterial elements, neutral inclusions, transparency and causality

Acoustic metamaterial elements based on cylindrical elastic shells with an internal mass supported by axisymmetric stiffeners are described. The shell's effective acoustic properties are tuned by varying the mass and stiffness. The elements can be impedance and index matched to water, resulting in near-zero scattering cross section over a broad range of low frequencies. The physical constraints necessary for low frequency transparency imply that the scattering is non-causal which means there must be scattering at high frequency.