Optimal feedforward control of a beam with an active acoustic black hole termination

Acoustic black holes are structural features that are realised by tapering the thickness of a beam or plate, usually via a power law profile. Practical acoustic black holes have been shown to significantly reduce vibrations at high frequencies when combined with a thin layer of passive damping but, due to design constraints on the taper length and tip height, passive designs are somewhat limited at lower frequencies. In this paper, an active solution has been investigated to control the low frequency vibration of a beam with an acoustic black hole termination. Piezoelectric patch actuators have been attached to the taper and unconstrained feedforward control has been simulated to minimise the kinetic energy of the uniform beam section. The effect that this control strategy has on the structural response has been investigated through a series of numerical simulations and the potential performance of an active acoustic black hole has thus been demonstrated.