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.