Concave-shaped acoustic black holes with asymmetric arrangement for suppression and amplification of structural vibration

Abstract

An acoustic black hole (ABH) is a wedge-shaped structure characterized by a power-law thickness profile with an exponent greater than or equal to two. In this study, we engineer an ABH with a concave shape, where both the width and thickness decrease according to power-law profiles. This configuration facilitates the focusing of elastic waves at the tip region with higher energy density than conventional constant-width ABHs. The highly focused waves are attenuated using a small amount of viscoelastic material attached near the tip of the ABH, resulting in dampened vibrations in the original structure such as a thin beam. Despite being about half the weight of the conventional ABH of equivalent length, the concave ABH achieves similar damping performance to the conventional one. When the conventional ABH is adjusted to match the weight of our concave design, the latter exhibits enhanced damping performance along with a lower cut-on frequency. Near-perfect reduction of structural vibration is attained by affixing a concave ABH to each end of the beam. By delicately adjusting their lengths and employing them asymmetrically, we manipulate the vibration mode shapes to minimize the structural vibrations. As a result, vibrations in the beam are barely perceptible under high-frequency harmonic excitation. The concave ABH, characterized by its ability to intensively focus elastic waves at its narrow and thin tip, is also suitable for vibration amplification, facilitating the detection of minute vibrations distributed in the original structure. The concave ABH offers improved performance in both wave absorption and amplification compared with conventional ABHs of the same length or weight, highlighting its potential as an alternative solution in vibration damping or sensing applications.