Characterization of acoustic black hole effect using a 1-D fully coupled and wavelet-decomposed semi-analytical model

Acoustics Black Hole (ABH) effect shows promising features for potential vibration control and energy harvesting applications by utilizing wave propagation properties in structures with diminishing thickness to gradually reduce the velocity of flexural waves. The unavoidable truncation introduced in manufacturing the tailored power-law profile of the ABH-featured structure has been shown to significantly weaken the ideal ABH effect, which can be compensated to a certain degree by adding a thin damping layer. The coupling between the tailored ABH part and the thin damping layer is then critical and not 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 thin damping layers coated over its surface. Highly consistent with FEM results, numerical results demonstrate that the proposed wavelet-based model is particularly suitable to characterize the wavelength fluctuation along the beam as a result of ABH effect. The model provides an efficient way to study the ABH effect on the vibration response of the beam. Due to its modular and energy-based feature, the proposed framework offers a general platform for embedding other control or energy harvesting elements into the model for investigating various ABH applications.