Numerical and experimental investigation of the acoustic black hole effect for vibration damping in beams and elliptical plates

Abstract

Flexural waves in beams and plates slow down if their thickness decreases. Such property\nwas successfully used for establishing the theory of acoustic black holes (ABH). In fact, in\nthe case of a sharpened edge having a power-law profile, it can be shown that the\nrefection coefficient of a wave propagating towards the sharpened edge can be equal to\nzero. However, manufacturing such profiles is always related to truncations and\nimperfections that undermine ABH. It is known though that the use of a thin absorbing film\ndrastically improves the damping effect of ABH. The aim of the current paper is to show\nnumerically and experimentally the capability of ABH to provide structural damping without\nintroducing additional mass. The dynamic behaviour of a non uniform Euler-Bernoulli beam\nis described using a Riccati equation for the beam impedance, which leads to the reflection\nmatrix of the sharpened edge of the beam. The influence of length of the profile, thickness\nand length of the absorbing film are evaluated as realistically as possible and optimised\nnumerically in order to reduce wave reflection from the edge. Keeping in mind the\nnumerical results, an elliptic plate with a pit of power law profile placed at one of its\nfocuses has been designed and tested. As a result, both numerical simulations and\nexperimental measurements show significant reduction of vibration levels.