The exact spectral element modeling and vibration analysis of the acoustic black hole double-beam system

Abstract

In this paper, we present a study of vibration characteristics of the double-beam structures combined with the concept of the acoustic black hole (ABH), which is an effective technique for vibration and noise control. In the proposed double-beam structure, the ABH beam as the vibration damper is attached to the primary uniform beam by a range of translational and rotational springs. We formulate the closed-form spectral element matrix of the double-beam structure and calculate the natural frequencies and mode shapes of the system. The results demonstrate the ABH effect of increasing the modal damping ratios. We also study the power flow and mechanical intensity of the system to offer physical insight into the vibration suppression mechanism of the ABH. A detailed parametric analysis of both translational and rotational springs is carried out. The investigation contributes to the exact dynamic modelling and analysis of the double-beam system containing ABH elements. Furthermore, the proposed ABH double-beam structure shows great potential for vibration control and energy harvesting.