Numerical investigation of simply supported periodic rectangular plates with acoustic black hole wedge

In this paper, we propose the periodic rectangle plate with one-dimensional acoustic black hole (ABH) wedge under the simply supported condition. The vibration performances have been investigated by the semi-analytic method based on the levy solution method combined with WKB approximation, which is also validated by finite element method (FEM) simulation. For the rectangle ABH wedge, we derive the flexural wave dispersive relationship in plate, which also revealed the cut-on frequency. It can also be found that with the increase of periodic number, the vibration of plate structure can be reduced not only in the high frequency range where traditional ABH effect takes effect, but in low and middle frequency range the periodic ABH wedge can also show its advantage. Meanwhile, the damping coupling performance between the periodic ABH wedge and attached damping layers has also been investigated to enhance the vibration reduction. This novel kind ABH structure shows its potential in engineering applications.