Concentration and attenuation of flexural vibrations in tapered cylindrical beams and wedge-like rectangular beams with power-law thickness

The Acoustic Black Hole (ABH) effect for vibration control and sound absorption can be realized in tailored structures with a power-law-profiled thickness variation as the wave velocity will gradually decrease to zero in an ideal scenario. This means that no reflection occurs since the bending wave are not able to arrive at the edge of ideal ABH structures. One merit of the ABH effect is that vibration energy can be completely captured at the tip of the wedge structures. This feature makes ABH structures have a great potential in the aspects of vibration reduction and energy harvesting. In this paper, in order to describe the energy focalization effect properly, the semi-analytical method will be used to established the dynamical model as it can describe the system in terms of vibration energy. The mean square velocity (msv) of some measuring points has been calculated to analyze the difference of the energy concentration effect between the tapered rod and the wedge-shaped beam. Numerical results reveal that both of them own similar effect on energy trapping. However, the energy density at the tip of the rod is obviously larger than that at the edge of the wedge beam, which denotes that adhering less viscoelastic materials on the edge of tapered rods can achieve similar energy concentration effect compared with wedge-shaped beams.