Ultra-broadband gaps of a triple-gradient phononic acoustic black hole beam

Drawing on the principles of energy convergence and local resonance, the acoustic black hole (ABH) emerges as a promising unit cell within phononic crystals (PCs). It has the potential to achieve superior wave attenuation and lightweight performance simultaneously. In this paper, we propose a novel triple-gradient phononic ABH beam and strategically manipulate multiple gradients in the thickness, density, and modulus to enhance broadband vibration reduction. To characterize the dynamic performance, complex band and vibration transmission analyses are conducted by the extended plane wave expansion (EPWE) method and hybrid dynamics method (HDM), respectively. Via the comparative assessments of wave attenuation capacity and transmission loss between various multiple-gradient and single-gradient beam configurations, it reveals that the ABH effect is not solely brought by thickness gradient but also extends to the power-law gradients in density and modulus. More importantly, the synergistic development of three different gradient effects can lead to more pronounced and broader bandgaps in PCs. Meanwhile, a comprehensive parametric study on the bandgap characteristics reflects the trade-off relationship between structural strength and vibration attenuation capacity. Consequently, a multi-objective nonline ar optimization model that integrates the EPWE method and NSGA-II algorithm, is carried out to determine the optimal parameters of the proposed structure. The optimization outcome not only demonstrates the exceptionally wide bandgap performance of the optimized structure, but also serves as a valuable design guideline for ABH metamaterials geared towards broadband vibration reduction.