Analysis of ray trajectories of flexural waves propagating over generalized acoustic black hole indentations

An Acoustic Black Hole (ABH) indentation embedded in thin-walled structures has been proved remarkably useful for broadband flexural wave focalization, in which the phase velocity of the flexural waves and the refractive index of the media undergo gradual changes from the outside towards the center of the indentation. A generalized two-dimensional ABH indentation can be defined by three geometric parameters: a power index, an extra thickness and a radius of a plateau at the indentation center. The dependence of the energy focalization on these parameters as well as the energy focalization process is of paramount importance for the understanding and design of effective ABH indentations. This work aims at investigating the energy focalization characteristics of flexural waves in such generalized ABH indentations. The calculation of the flexural ray trajectories is conducted to reveal and analyze the wave propagation features through numerical integration of the eikonal equation from the Geometric Acoustics Approximation (GAA). The theoretical results are verified by both experiment using wave visualization technique based on laser acoustic scanning method and finite element (FE) simulations. Finally, the influence of the geometric parameters on the flexural wave focalization characteristics in ABH indentations is discussed in detail.