Passive constrained viscoelastic layers to improve the efficiency of truncated acoustic black holes in beams

Power-law profiles at the edges of beams and plates have proved to be a very efficient way to attenuate vibrations. In an ideal scenario, for a profile with zero end thickness, the energy of flexural vibrations would never reflect from the boundaries, giving place to the Acoustic Black Hole (ABH) phenomenon. In practice, however, the edge must be truncated which results in a non-zero reflection coefficient. To partially mitigate this problem, a viscoelastic layer (VL) is typically placed at the tip of the ABH termination to compensate for the effects of truncation. Instead, in this work it will be shown that one can achieve better results by resorting to passive constrained viscoelastic layer (PCVL). The latter consists of a sandwich made of a viscoelastic layer (VL) plus a constrained layer (CL). An analytical model is developed to describe the performance of a truncated ABH beam with PCVL, where the displacement fields are expanded by means of Gaussian functions. The model is validated through finite element (FEM) simulations and experiments. It is observed that a truncated ABH beam with PCVL at the tip performs better than an ABH beam with an unconstrained VL, even if they add equal mass to the system.