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

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