Quantitative analysis of acoustic black hole property by the catastrophe theory.

• Combination of acoustic black hole structure with the catastrophe theory. • Elaboration of the relationship between each parameter of the acoustic black hole and the energy aggregation effect. • Achievement of the quantitative analysis of the acoustic black hole. • Theoretical verification is carried out by simulation. Acoustic black holes (ABHs) have garnered increasing attention in the field of vibration and noise reduction due to their excellent wave aggregation effect. A large number of studies have been conducted in analyzing ABH structures, these analytical methods such as finite element and semi-analytical modeling, however, still suffer from limitations in the quantitative analysis of ABHs. The majority of the existing methodologies are intricate and computationally burdensome and do not furnish a quantitative assessment of the ABH structure. To meet this need, we design a theoretical analysis model from the catastrophe theory perspective. Based on the Hyperbolic umbilic model, the proposed analytical method can investigate the quantitative relationships among each parameter and their energy aggregation effects in ABHs. Combined with a dimensionless analytical solution, the underlying mechanism and the quantitative property of ABHs are expected to be revealed with significantly reduced computational complexity. Further, the proposed quantitative method is demonstrated by a numerical simulation test and a practical experiment. The findings illustrate a clear presence of a catastrophe effect across the range of ABH parameter variation, and establish a direct correlation between each ABH parameter and the ABH effect in the proposed approach. The proposed theoretical method holds significant potential in analyzing and applying of ABHs. [Display omitted] [ABSTRACT FROM AUTHOR]