Characterization of acoustic black hole effect using a one-dimensional fully-coupled and wavelet-decomposed semi-analytical model

Acoustics Black Hole (ABH) effect shows promising features for potential vibration control and energy harvesting applications. The phenomenon occurs in a structure with diminishing thickness which gradually reduces the phase velocity of flexural waves. The coupling between the tailored ABH structure and the damping layer used to compensate for the adverse effect of the unavoidable truncation is critical and has not been well apprehended by the existing models. This paper presents a semi-analytical model to analyze an Euler-Bernoulli beam with embedded ABH feature and its full coupling with the damping layers coated over its surface. By decomposing the transverse displacement field of the beam over the basis of a set of Mexican hat wavelets, the extremalization of the Hamiltonian via Lagrange׳s equation yields a set of linear equations, which can be solved for structural responses. Highly consistent with the FEM and experimental results, numerical simulations demonstrate that the proposed wavelet-based model is particularly suitable to characterize the ABH-induced drastic wavelength fluctuation phenomenon. The ABH feature as well as the effect of the wedge truncation and that of the damping layers on the vibration response of the beam is analyzed. It is shown that the mass of the damping layers needs particular attention when their thickness is comparable to that of the ABH wedge around the tip area. Due to its modular and energy-based feature, the proposed framework offers a general platform allowing embodiment of other control or energy harvesting elements into the model to guide ABH structural design for various applications.