Nonlinear features and energy transfer in an Acoustic Black Hole beam through intentional electromechanical coupling

Acoustic Black Hole (ABH) phenomenon features unique wave retarding and energy focusing of flexural waves inside thin-walled structures whose thickness follows a power-law variation. Existing studies, mostly focusing on linear aspects, show the deficiency of the linear ABH structures in coping with low-frequency problems, typically below the so-called cut-on frequency. In this paper, electrical nonlinearities are intentionally imposed via PZT patches over an ABH beam to tactically influence its dynamics through electromechanical coupling. Using a fully coupled electromechanical beam model, typical electromechanical coupling phenomena between the beam and the external nonlinear circuits, as well as the resultant salient nonlinear features of the system, are numerically investigated. Results show the beneficial effects arising from the intentional electrical nonlinearity in terms of generating energy transfer from low to high frequencies inside the beam, before being dissipated by the ABH covered by a small amount of damping materials. As such, the effective frequency range of the ABH is broadened, conducive to low frequency vibration control problems. Meanwhile, different from existing mechanical means, the introduced intentional electrical nonlinearity allows for flexible tuning to accommodate specific frequency ranges arising from different applications.