Ultra-low frequency broadband gap optimization of 1D periodic structure with dual power-law acoustic black holes

The acoustic black hole (ABH) structure has gradually become a research hotspot in recent years due to its ascendant capacity of vibration attenuation and energy accumulation. To further improve the performance of vibration and noise reduction, the ultra-low frequency broadband gap of a one-dimensional structure embedded ABHs with power-law material properties is investigated in this paper. Based on the Euler-Bernoulli theory, the Transfer Matrix Method (TMM) is used to establish the dynamic model of the dual power-law ABH (DP-ABH) beam. The band structure results obtained by TMM and the finite element method are compared with each other to verify the ultra-low broadband gap of the structure. Comparison with the traditional ABH show that the ultra-low frequency performance of the DP-ABH is due to the enhanced local resonator properties with reduction of dual power-law local stiffness. Parameter analysis served as a guide for optimization is carried out and a method of combining NSGA-II and TMM is applied to optimize the ABH section with full parameters, to consider a trade-off between lower bandgaps and higher stiffness. The investigation shows that the ultra-low broadband gaps of the periodic DP-ABHs structure, which meets adequate stiffness requirements, can be designed by optimized configuration.