An analytical study on bending wave reflection at interface between beam and curvilinear acoustic black hole

Abstract

Acoustic Black Hole (ABH) is a thin structure that is tapered according to the power-law profile of power greater than or equal to two. ABH dampens the vibration of plates or beams by slowing and attenuating the bending waves incident upon the ABH. Recently, we proposed a design of ABH that utilizes a spiral baseline instead of the ordinary straight baseline in order to enhance the space efficiency while preserving the damping performance. In this study, the underlying physics of our previous result using an analytical approach is investigated. The reflection coefficient of bending waves at the interface between a straight beam and standard ABH with taper power of two is first investigated by using the exact solutions of wave motion in the waveguides. To be specific, the effect of tip thickness, tip truncation, and material loss factor on the reflection coefficient is investigated. Then, the analytic reflection coefficient of curved beams with various curvatures are investigated. Finally, to consider the effect of tapered geometry and curved geometry simultaneously, the governing equation of ABH with constant curvature is formulated. Consequently, this study aims to theoretically support the damping performance of an Archimedean spiral ABH in our recent work.