Tunable tri-band negative mass density acoustic metamaterials with nested three-layer hollow tubes

Abstract

To relieve the bulkiness of the structures of multiband acoustic metamaterials in isolation applications, a nested three-layer hollow tube (NTLHT) structural unit is presented in this work. This unit was designed to achieve effective acoustic isolation at three different frequency bands. Furthermore, a precise theoretical formula for the resonance frequency was derived by combining the 1D wave approximation principle with the coupling interaction. Three-band acoustic metamaterials with high-performance sound isolation were prepared using the NTLHT structural unit by combining three approaches: simulation, theory and experimentation. The results show that the NTLHT can form three independent transmission-forbidden bands under the condition l₁>l₂>l₃, whereas the relative tube position of the NTLHT has no effect on the transmission-forbidden band, resulting in high engineering fault tolerance. The forbidden frequency exhibits a redshift with increasing the length or effective cross-sectional area of each tube layer. The theoretical and simulated resonance frequencies are in good agreement; therefore, the geometrical parameters of the structural unit corresponding to the target isolation band can be obtained from the accurate theoretical formula. Thus, the nested tri-band metamaterials with high-performance acoustic isolation can be further custom-designed in three specific frequency bands, and the structure is expected to be used in a wide range of acoustic isolation applications.