Measurement and modelling of the reflection coefficient of an Acoustic Black Hole termination

The flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered with a power law profile and covered by a thin layer of additional damping material. Such a termination induces the so-called “Acoustic Black Hole effect” (ABH): 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. This paper presents a specific study of the reflection coefficient of ABH beam terminations. A Kundt-like measurement method of the reflection coefficient of a beam termination is proposed. The method is validated using theoretical results in the case of a beam free end. Results for several ABH extremities show a clear decrease of the modulus of the reflection coefficient R. The phase of R due to the decreasing thickness profile is also investigated and is interpreted by defining a correction length for the tapered termination. These experimental results are compared with several models: geometrical acoustics based model, beam waveguide model and plate model.