Wave propagation and vibration attenuation in spiral ABH metamaterial beams

Metamaterials with low-frequency and broadband bandgaps have great potential for manipulating elastic/ acoustic waves. Inspired by the frame structures that are widely used in engineering and the acoustic black hole (ABH) structure with extraordinary properties of wave manipulation and energy focalization, a novel metamaterial beam with spiral ABH resonators is proposed, which can cover nearly 63 % of the frequency range of 0-1100 Hz based on local resonance mechanism without degrading the strength and stiffness of the main structure. The dispersion relation and eigenmodes of low-frequency bandgap boundary are analytically derived, which provides explicit guidance for the adjustment of the bandgap characteristics. Compared with the metamaterial beam with rod mass resonators, the spiral ABH resonators have a larger energy proportion and better capacity for energy concentration. Furthermore, the results show that decreasing the base thickness of spiral ABHs can form the bandgap in the low-frequency range of 39-53 Hz. Increasing the tip thickness or base thickness of the spiral ABHs allows the tuning of the bandgaps to enlarge the bandgaps, which can exceed 50 % of the frequency range of 0-400 Hz. Due to the strong designability of the distribution and the number of spiral ABH resonators, the structure with ABH in the corners of the frame can cover 71.3 % of the 0-1100 Hz. Experimental results show that with only three cells, the proposed metamaterial beam allows considerable vibration attenuation within a broad frequency range, especially in the low-frequency range (167-235 Hz), and it can transfer and dissipate the vibration energy from the main beam to avoid large deformations in the frame, which conventional frame beam can hardly reach. This study provides new guidance for structural design and engineering applications of metamaterial beams.