Reflexion of flexural waves at the end of a tapered beam of quadratic profile covered with a thin viscoelastic layer

Abstract

Flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered with a power law profile and covered by a very thin viscoelastic layer [Krylov, JSV 274, 605–619 (2004)]. Such a terminaison induces an effect known as “the acoustic black hole effect” (ABH), which is resulting from properties of propagation of flexural wave in beams having non homogeneous thicknesses: if the thickness decreases locally, flexural waves slow down and the amplitude of the displacement field increases, leading to efficient energy dissipation if an absorbing layer is placed where the thickness is minimum [Georgiev et al., JSV 330, 2497–2508 (2011)]. Absorption of the ABH terminaison is estimated, thanks to the direct measurement of the reflexion coefficient, using a wave decomposition technique. Experimental modal analysis of a ABH beam can be performed using a “high resolution” technique, which permits to estimate the modal density. Analysis of these experimental results is performed, thanks to a model based on the finite difference method. It is shown that local transverse modes are playing an important role in the absorption properties of ABH.