A Virtual Acoustic Black Hole on a Cantilever Beam

TL;DR

This paper introduces a digital control-based virtual acoustic black hole (VABH) that mimics a mechanical ABH to localize and dissipate vibrational energy on a cantilever beam, overcoming physical constraints of traditional ABHs.

Contribution

It proposes and demonstrates a novel digital control approach to create a VABH, extending the applicability of acoustic black holes without mechanical limitations.

Findings

VABH effectively localizes vibrational energy on a cantilever beam.

Experimental results confirm the VABH's performance matches theoretical predictions.

VABH broadens the practical use of ABH concepts in structural vibration control.

Abstract

An acoustic black hole (ABH) consists of a tapered structure whose thickness follows a power-law profile. When attached to a host structure, an ABH localizes and traps the vibrational energy, which can then be dissipated through, e.g., a damping layer. However, effective vibration mitigation is known to occur only above a cut-on frequency which is inversely proportional to the length of the tapered structure. In this context, the main thrust of this paper is to replace a mechanical ABH by a digital controller so as to create a so-called virtual acoustic black hole (VABH), thus, freeing the ABH from possible mechanical constraints (e.g., compactness, manufacturing and fatigue issues). The proposed VABH is first detailed theoretically. The salient features and performance of the VABH are then demonstrated both numerically and experimentally using a cantilever beam as a host structure. Eventually, it is shown that the VABH significantly enlarges the applicability of the concept of an ABH.