Optimization of the Geometric Characteristics of Damping Layers for Acoustic Black Hole Beams Based on the Backpropagation Algorithm

In real-world scenarios, it is common to apply a damping layer of a specific thickness to the surface of an acoustic black hole (ABH) beam to boost its energy dissipation capacity. However, it has become apparent that excessive damping layers might result in negative consequences. The present study suggests employing the backpropagation (BP) algorithm to refine the positioning, thickness, and contour of the damping layer for optimal results. This study begins with the derivation of a semi-analytical solution for the vibration characteristics of an ABH beam under a harmonic load using the Gaussian expansion method (GEM). This process results in the preliminary identification of a thickness profile for the damping layer that exhibits significant potential for energy dissipation. Subsequently, a BP neural network is trained on the data produced by the semi-analytical solution to further optimize this thickness variation function. The findings reveal that the geometry of the damping layer has a more complex influence on performance than previously recognized. The optimization guided by the BP neural network suggests that achieving a strong ABH effect does not require uniform application of the damping layer across the entire ABH section. Rather, the most effective approach is to concentrate the damping layer thickness at the ABH tip, with a rapid decrease in thickness as one moves away from this point. It is also determined that applying a damping layer in areas far from the tip is unnecessary. Additionally, an innovative strategy is proposed to enhance the system’s energy dissipation capabilities without changing the truncation thickness of the ABH beam. This research contributes to a deeper understanding of how the damping layer affects the energy dissipation performance of ABH beams.