Wave propagation in a honeycomb sandwich panel of variable thickness: model and characterisation of the Black Hole Acoustic effect

Abstract An Acoustic Black Hole (ABH) is a scatterer, embedded in a panel, allowing passive vibration control without adding mass. In practice, it is achieved by means of a local reduction in thickness (axisymmetric pit with a parabolic profile) and the addition of a thin viscoelastic coating in a central region of uniform thickness (plateau). The vibration absorption induced by the ABH, allows the design of stiff, light and non-resonant panels. In this paper, we propose to study this effect for a three-layer sandwich panel (glass fiber skin/honeycomb core/glass fiber skin), which gives rise to both bending and shear effects. The equations of motion of the thick, symmetrical sandwich panel with variable characteristics is obtained within the framework of the zig-zag theory by applying Hamilton’s principle. These equations lead to a sixth-order analytical model, allowing the dispersion curves to be obtained, and then an analytical model of the scatterer inserted in an infinite panel. The analysis of the local modes of the scatterer allows the evaluation of its absorption; the interpretation of the ABH effect is carried out using its scattering matrix. The model allows in particular the analysis of the effect of shear on the ABH effect. Experimental tests, based on vibrational maps obtained by vibrometry, are used to discuss and validate the predictions.