Ultra-Low-Frequency Acoustic Black Hole Radial Elastic Metamaterials

In this paper, we propose an acoustic black hole radial elastic metamaterial (AREM). Through the study of its dispersion relations, it is found that, compared with the conventional elastic metamaterial, the AREM gathers energy at the tip of the black hole cell, which can trigger the local resonance (LR) effect and couples with the Bragg scattering (BS) effect, thus opening the very low-frequency strong attenuation broadband. The influence of the structural parameters of the AREM on the bandgap (BG) characteristics is further explored, and the bandwidth can be modulated in the frequency range of 0-1300 Hz by varying the truncation thickness and power exponent of the acoustic black hole (ABH) structure. Finally, by analyzing the transmission spectrum and displacement field, it is found that the total bandwidth of the flexural BG is better than that of the conventional radial elastic metamaterial, and the wave attenuation capability is improved by more than 110%. It is also discovered that the BG characteristics of the longitudinal BG are also better than those of the conventional radial elastic metamaterial, and the total bandwidth of the longitudinal BG is superior to that of the conventional radial elastic metamaterial, with the wave attenuation capability improved by more than 56%. The research findings may have applications in engineering fields such as ultra-low-frequency vibration reduction.