Elliptical acoustic black holes for flexural wave lensing in plates

Circular acoustic black holes (ABHs) on plates help reducing overall vibrations by concentrating them at the ABH centers, where vibrations get dissipated by means of viscoelastic layers. However, in many practical situations one may be interested in focusing energy outside the ABHs, at regions of the plate with constant thickness. To date, this has only been achieved in the ABH framework by exploiting properties of phononic ABH arrays. However, easier solutions exist for energy focusing based on gradient refraction index materials, like Luneburg-type lenses. In this line, an elliptical acoustic black hole (EABH) lens is proposed in this work that can concentrate waves at a predefined focal point and which only involves slight thickness reduction, as opposed to requirements in most ABH applications. The performance of EABHs on plates is characterized with two approaches: the geometrical acoustic method (GAM) that determines ray trajectories, and the Gaussian expansion method (GEM) which allows one to compute the plate's flexural wave displacement field. Both methods are validated against finite element simulations. Moreover, a detailed study of the variations in focal distance and wave amplitude at the focal region depending on the EABH parameters is presented. The usefulness of setting several EABHs in parallel is also analyzed. The proposed EABH broadens the potential for energy harvesting applications avoiding the wavelength-shortening effect inside ABHs and offers new possibilities for acoustic imaging.