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

Acoustic Black Holes (ABHs) are structural features that are typically realised by introducing a tapering thickness profile into a structure that results in local regions of wave-speed reduction and a corresponding enhancement in the structural damping. In the ideal theoretical case, where the ABH tapers to zero thickness, the wave-speed reaches zero and the wave entering the ABH can be perfectly absorbed. In practical realisations, however, the thickness of the ABH taper and thus the wave-speed remain finite. In this case, to obtain high levels of structural damping, the ABH is typically combined with a passive damping material, such as a viscoelastic layer. This paper investigates the potential performance enhancements that can be achieved by replacing the complementary passive damping material with an active vibration control (AVC) system in a beam-based ABH, thus creating an active ABH (AABH). The proposed smart structure thus consists of a piezo-electric patch actuator, which is integrated into the ABH taper in place of the passive damping, and a wave-based, feedforward AVC strategy, which aims to minimise the broadband flexural wave reflection coefficient. To evaluate the relative performance of the proposed AABH, an identical AVC strategy is also applied to a beam with a constant thickness termination. It is demonstrated through experimental implementation, that the AABH is able to achieve equivalent broadband performance to the constant thickness beam-based AVC system, but with a lower computational requirement and a lower control effort, thus offering significant practical benefits. (paper)