Enhanced Acoustic Black Hole effect in beams with a modified thickness profile and extended platform

The phenomenon of Acoustics Black Hole (ABH) benefits from the bending wave propagating properties inside a thin-walled structure with power-law thickness variation to achieve zero reflection when the structural thickness approaches zero in the ideal scenario. However, manufacturing an ideally tailored power-law profile of a structure with embedded ABH feature can hardly be achieved in practice. Past research showed that the inevitable truncation at the wedge tip of the structure can significantly weaken the expected ABH effect by creating wave reflections. On the premise of the minimum achievable truncation thickness by the current manufacturing technology, exploring ways to ensure and achieve better ABH effect becomes important. In this paper, we investigate this issue by using a previously developed wavelet-decomposed semi-analytical model on an Euler-Bernoulli beam with a modified power-law profile and an extended platform of constant thickness. Through comparisons with the conventional ABH profile in terms of system loss factor and energy distribution, numerical results show that the modified thickness profile brings about a systematic increase in the ABH effect at mid-to-high frequencies, especially when the truncation thickness is small and the profile parameter m is large. The use of an extended platform further increases the ABH effect to broader the frequency band whilst providing rooms for catering particular low frequency applications.