Tunability of the resonant modes of an Acoustic Black Hole embedded in an infinite thin plate

A two dimensional circular Acoustic Black Hole (ABH) is a wave trap used to passively control the vibrations of a panel. It consists of a local thickness reduction made by an axisymetric pit of a profile at least quadratic. A thin viscoelastic coating in the central area can give rise to an efficient damping mechanism. Such ABH inserted in an infinite thin plate behaves as a resonant penetrable scatterer whose resonant modes correspond to the free oscillations of the system. They are characterized by complex eigenfrequencies and complex eigenshapes due to the fact that it is a resonant open system. The relation between the real and the imaginary parts of the eigenfrequencies describes the leakage effects of the AB. Among all the resonances, the first one is of great interest for controlling the vibration damping at selected low frequencies. In this work, the tunability of the first trapped mode is studied by modifying the classical ABH geometry. The parametric study is considers the frame of the Kirchhoff model of a thin plate of local varying thickness. A semi-analytical model based on the multiple scattering theory is used to evaluate the effect of the geometrical modifications on the scatterer. Experiments from a scanning laser vibrometer set up also illustrate the modal behavior. The design shown in this work and the obtained results motivate the use of the resonant ABH as resonant building blocks of a locally resonant plate, also know as metaplate, for low frequency wave control.