Realization of a Virtual Acoustic Black Hole with Piezoelectric Patches

Abstract

Reducing the mechanical vibration is of the utmost importance to lower mechanical stress and thus extend the life of a structure. This work proposes a novel concept to achieve this through an acoustic black hole (ABH) effect implemented via a digital controller. An ABH is a device that localizes the vibrational energy, which is in turn dissipated using damping layers. Its practical realization consists of a tapered wedge beam whose thickness follows a power-law profile. Its efficiency usually starts beyond a cut-on frequency, which is inversely proportional to its length. Obtaining the ABH effect on slender structures is thus very challenging: to achieve vibration reduction at low frequencies, the tapered wedge beam must be very long and thin. We propose herein to circumvent this problem by using a digital controller connected to piezoelectric transducers which are bonded to the host structure. Digital controllers have the significant advantage of being able to reproduce virtually any desired mechanical impedance function and, in particular, that of an ABH. We verify the soundness of the approach through detailed numerical simulations. Those are conducted on a one-dimensional slender beam modeled by the finite element method. The simulations show promising results, and the practical realization of the virtual acoustic black hole (VABH) is discussed eventually.