Beam-type acoustic black holes incorporating the microstructure-dependent nonlocal effect

Abstract

Acoustic black holes (ABHs) are effective passive damping structures for capturing bending waves at wedge edges. However, as the wedge shape continuously reduces in size, the intrinsic length scale of the ABH's tip gradually approaches the external length scale, such as the wavelength of wave, which causes a phenomenon known as the "scale effect" to take hold of the ABH. Despite gaining considerable attention in the past two decades, the influence of intrinsic length on the energy aggregation of ABHs has not been thoroughly investigated. This study aims to explore the significant contribution of microstructure-dependent nonlocal effects on the dynamic behavior of ABHs, which holds great scientific importance. The nonlocality arises from the inherent length of the material being studied. A nonlocal elastic theory (NET) is employed to model the dynamic behavior of one-dimensional ABH beams. Geometric acoustic method is proposed to analyze the power-law beam wave number and microstructure-related reflection coefficient. Results indicate a significant impact of nonlocality on the acoustic energy of beam-type ABHs, particularly when the nonlocal intrinsic length approaches the truncation length of the wedge. Moreover, a comparison between the present study and classical theory reveals an overestimation of the reflection coefficient in conventional works for small truncation lengths. The relationship between the reflection coefficient, truncation length, and nonlocal characteristic lengths is thoroughly examined. Additionally, the influence of the damping layer and different power-law exponents m on ABH behavior is extensively studied.