The Use of Perfect Absorption in the Tunability of the Resonant Modes of an Acoustic Black Hole

An Acoustic Black Hole (ABH) is a wave trap used to avoid edge reflections of flexural waves in plates or beams. It consists of reducing the thickness in specific areas by using an axisymmetric pit which is, at least, quadratic. Adding a thin viscoelastic coating in its central area can give rise to an efficient damping mechanism. Such ABH can be seen as resonant penetrable scatterers with resonance modes. Since the ABH is a resonant open system, its modes are characterized by complex eigenfrequencies whose the imaginary parts are related to the leakage of the mode into the plate. In this work, we discuss the balance between the losses arising from viscoelastic coating and the leakage of the first trapped mode to fulfill the perfect absorption condition. Of particular interest is the critical coupling condition which occurs when the losses coming from the viscoelastic coating balance the leakage of the first trapped mode. This results in an absorption coefficient of the ABH equal to 1. The classical ABH geometry is also modified for this study in order to tune the first trapped modes. To these ends, a 1D semi-analytical model of beam is employed and experimental results will be shown.