The modeling of acoustic black hole beam by spectral element method

A technique developed in recent decades for the passive control of vibrations and noise is the Acoustic Black Hole (ABH). The structural ABH effect is achieved by incorporating a local modification in the thickness of a thin structure, typically a beam or a plate, with a variation in thickness according to a spatial power law. The combination of the variation in the thickness power law and a local increase in damping, provided by the concomitant application of layers of viscoelastic material, produces a significant reduction in the wave propagation speed and an increase of attenuation properties. As an elastic wave propagates within an ABH, its propagation speed decreases smoothly and continuously, in theoretical case, when the structure's thickness disappears at the end of the ABH, the wave speed drops to zero. For practical applications, ABH is typically combined with dissipative materials to obtain significantly higher structural loss factors. This work aims to establish a numerical approach for modeling and designing a beam-type structural one-dimensional ABH device for vibration control device using the Spectral Element Method (SEM) and verified by the Finite Element Method (FEM). Examples are performed, and the results are compared with those found in the literature.