Tri-Band Negative Modulus Acoustic Metamaterial With Nested Split Hollow Spheres

We presented tri-band negative modulus acoustic metamaterials (AM), whose operation characteristics could be flexibly designed by changing the three hole sizes (i.e., a1, a2, and a3) of the tri-layer nested split hollow spheres (NSHSs). We demonstrate numerically that tri-band negative modulus can be obtained and each resonant frequency corresponds to the hole size of each split hollow sphere. However, for the case when a1> a2> a3, the negative modulus band in the high frequency region vanishes. An effective sound-force analogue model with coupling interaction is further developed for the accurate prediction of the three resonant frequencies based on equating the tri-layer NSHSs to three spring oscillators in series. As a result of the analytical formulas, three resonant frequencies could be precisely controlled, and a nested AM with a tri-band negative modulus can be flexibly constructed. The proposed AM could be easily extended to multiple operation bands and can be further coupled with negative mass density structures for constructing multi-band double-negative AMs.