Flexural wave concentration in tapered cylindrical beams and wedge-like rectangular beams with power-law thickness

Abstract

The Acoustic Black Hole (ABH) effect is the phenomenon in which the wave velocity gradually decreases to zero when the bending wave propagates in wedge-like structures, such that no reflection occurs. This means that in the ideal scenario, flexural wave not reflects and the energy is totally captured at the tip of the wedge structure. ABH structures have great potential in the fields of vibration control and energy harvesting due to this phenomenon. In this paper, the semi-analytical method is adopted to establish the dynamical model of the one-dimensional cylindrical beam with ABH feature and arbitrary boundary condition. In order to investigate the effect of energy aggregating, the proportion of the kinetic or stain energy trapped in the arbitrary vicinity of the edge, as compared to that of the whole beam is defined and analyzed in detail. The main purpose of this paper is to analyze the different energy concentration effect between the tapered cylindrical beam and the wedge-like rectangular beam and hence to provide guidance for their applications in vibration control and energy harvesting. Numerical results show that considerable kinetic and strain energy are collected either in the tapered cylindrical beam or in the wedge-like rectangular beam. However, the energy density at the tip of the tapered cylindrical beam is obviously larger than that at the edge of the wedge-like rectangular beam. This means that vibration attenuation is increased when the same amount of viscoelastic material is adhered to the tip of the tapered cylindrical beams compared to the case of the wedge-like rectangular beams. Moreover, changing the excitation location on the tapered beam can also enhance energy concentration for different frequency bands. The theoretical model developed and new findings in this paper give rise to innovative applications of ABH beam structures in engineering and open new horizons to explore in the future.