Cut-off frequency for curvilinear acoustic black holes

Abstract

Acoustic black hole (ABH) is a thin wedge-shaped structure whose thickness profile is tapered according to the power-law with power greater than or equal to two. Due to its geometry, the ABH slows down the group speed of incident flexural waves, thereby focusing the wave energy on its tip. Recently, a new design of the ABH with baseline in curvilinear shape was proposed in order to enhance the space efficiency while maintaining the wave attenuation performance. By means of numerical simulations, it was shown that the damping performance of the ABH was maintained above a certain critical frequency, the 'cut-off frequency'. Although the proposed curvilinear ABH is a compact and effective solution to vibration damping in thin beams and plates, it is important to avoid using the curvilinear ABH below the cut-off frequency since the damping performance of the curvilinear ABH is not the same as that of the straight conventional ABH. In this study, by modeling the wave motion within the curvilinear ABH mathematically, we investigate the cut-off frequency for curvilinear ABHs. Specifically, we investigate the effect of geometrical parameters on the cut-off frequency for the arc ABHs and the spiral ABHs. This study ultimately aims at designing space-efficient curvilinear ABHs suitable for various industrial applications.