Optimal design and position of an embedded one-dimensional acoustic black hole

Structures whose thickness is tapered according to a power law exhibit the 'acoustic black hole' effect, and can be used for effective vibration reduction without adding mass. In this paper, we consider the problem of a one-dimensional acoustic black hole (ABH) with a free damping layer, embedded in a simply-supported beam which is excited by a harmonic force. The objective is to find the ABH design and position along the beam that simultaneously minimize the surface averaged square velocity response of the beam and the total mass of the beam. To determine the optimal design and position, a multi-objective evolutionary algorithm has been coupled with an automated meshing algorithm and commercial finite element software. The input variables are the taper profile of the ABH, the amount of damping, and the position of the ABH along the beam. Results of the optimization indicate that competition between design criteria exists, but only below a certain threshold. Optimization-based techniques like this can be applied to ABH design for more complex structures and can prove a valuable resource for noise control engineering.