Sound radiation of a beam with a wedge-shaped edge embedding acoustic black hole feature

As a potential intelligent structure which is capable of concentrating energy into local area, the Acoustic Black Hole (ABH) structure has high potential of application for sound radiation control. The ABH effect is caused by the infinitely small material attenuation in an inhomogeneous medium, such as the wedge-shaped beam with a diminishing thickness, giving rise to the reduction in the bending wave speed and no wave reflections in the tip. Therefore, the waves will be trapped in the edge portion. This paper investigates sound radiation problems of a beam embedding an ABH feature, focusing on characterizing and improving the low frequency performance of the beam on sound radiation reduction. The ABH beam is modeled and solved by transfer matrix method (TMM). Analytical solutions of vibration, wavenumber domain analysis and acoustic radiation phenomena are presented. A critical mode with very high order of the ABH beam is found, resulting in that its radiation efficiency is lower than that of the uniform beam in a specified range of frequencies. Generally, the low frequency performance will be improved effectively by enhancing the interaction between the bending waves and ABH element.