Analysis on vibration energy concentration of the one-dimensional wedge-shaped acoustic black hole structure

Abstract

The transverse vibration energy of a plate with a wedge-shaped profile can be trapped by acoustic black hole effect to its edge portion, in case the wedge thickness is diminished according to the power-law h(x) = εxm with m ≥ 2.0. The acoustic black hole effect exhibits potential ability for passive vibration control and energy harvesting. In this article, the transfer matrix method is adopted to establish and solve the dynamical model of acoustic black hole structure. Energy ratio is defined as a ratio of the energy trapped within the edge portion to that of the whole wedge, to illustrate the energy concentration effect. Analyses show that both the strain energy ratio and kinetic energy ratio of the acoustic black hole structure achieve the minimum when the wedge is in resonances, although these two kinds of energy come to peaks at this case. However, in the case of small length of the edge portion, the strain energy ratio reaches the highest peaks at the second and higher resonances, rather than at the first one. Generally, the best effect of energy concentration occurs when m ranges from 2.5 to 3.0. Reducing the truncation thickness and increasing the maximum height can improve the energy trapping.

Dynamic analysis and optimization of a cantilevered beam with both the acoustic black hole and the nonlinear energy sink

“…There are several configurations for NES and ABH effect respectively. For example, the grounded Ahmadabadi and Khadem (2012) and the ungrounded Parseh et al (2015) for NES, the conventional Li and Ding (2018) and the double-leaf Zhou et al (2017) for ABH. Although the conventional ABH structure with small truncated thickness may lead to strain/stressinduced fatigue issues, the studies on the 1D ABH structure are still of great interest, such as vibration control and band gap design.…”

“…In this example, we study the ABH effect on the vibration control of the NES. In Li and Ding (2018), the authors have shown that the ABH beam has excellent capability for energy concentration and the energy is transferred to the ABH part. This feature has an impact on the NES efficiency because the NES is very sensitive to the large displacement.…”

Acoustic Black Holes in Structural Design for Vibration and Noise Control

“…This indicates that the m value has a maximum limitation. Another theoretical and numerical study on vibration energy concentration of the 1D ABH was developed by Li and Ding [59]. The length of the edge part with comparatively large deflection deformation L e , as show in Figure 41, was investigated.…”

“…Schematic in 1D shows the ABH length of the edge part with a comparatively large deflection deformation Le. Adapted from[59]. Copyright SAGE Publications, 2018.…”

Active feedforward control of flexural waves in an Acoustic Black Hole terminated beam

“…The 'Acoustic Black Hole' (ABH) effect is a mechanism for attenuating flexural vibrations in structures, such as beams [1,2,3,4,5,6,7,8,9] or plates [10,11,12,13,14,15,16,17,18,19,20] and inherently provides a lightweight vibration control solution. Although the term 'Acoustic Black Hole' has a number of definitions in different fields, this paper focuses on the structural design feature that aims to control flexural structural waves.…”