Broadband vibration suppression of rainbow metamaterials with acoustic black hole

Acoustic black hole (ABH) structures have been widely utilized for vibration suppression owing to its tailored indentations according to a power-law profile. Compared with single ABH element, multiple ABHs embedded in periodic lattice configurations exhibit more remarkable attenuation effect within the so-called bandgaps at relatively low frequencies. However, most research is devoted to the analysis of uniform metamaterial embedded with periodic arrangement of ABHs, resulting in the attenuation bandgaps limited to a narrow frequency range. In this research, a rainbow metamaterial beam embedded with graded arrangement of ABHs is proposed to achieve broadband vibration attenuation. Two arrangement types of ABHs in metamaterial beams including linear and sinusoidal profiles are taken into account. The differential quadrature method is used to establish governing equations of infinite beams with periodic ABHs and finite rainbow metamaterials with graded ABHs, respectively. Using the validated mathematical model and genetic algorithm, wave propagation behaviors in infinite metamaterial beams, transmittance characteristics and optimization of finite rainbow metamaterial beams are investigated quantitatively. The results reveal that the generation of broad bandgaps can be explained by the combination of local resonance and Bragg scattering effects for proposed metamaterial beams with periodic asymmetrical ABHs. The corresponding bandgaps are tunable by changing the geometry parameters of ABHs. Moreover, the rainbow metamaterial beams with linear and sinusoidal ABHs own a broader attenuation band and better attenuation effect compared to the periodic ones. Compared with regular graded distributions, disordered arrangement of geometry parameters of neighboring cells leads to further improvement of attenuation strength. This work provides novel perspectives on achieving broadband vibration attenuation by rainbow metamaterial beams with ABHs, and the results could be applied to guide the design of rainbow metamaterial with graded geometry parameters.