Tunable shunting periodic acoustic black holes for low-frequency and broadband vibration suppression

Acoustic Black Holes (ABH) embedded within structures can efficiently damp vibrations above the cut-on frequency but fails below it, particularly when the flexural wavelength exceeds the size of the ABH. Therefore, addressing low-frequency vibration mitigation becomes imperative. Periodic ABH structures and shunt damping have been employed individually and proved effective, yet their combined application has not been explored previously. This paper introduces a novel approach for broadband vibration mitigation. It combines a periodic ABH beam, damping layer, and a resonant element comprising a piezoelectric patch and an inductance–resistance shunting circuit (referred as lossy PZT-ABH metabeam). This design addresses the shortcomings in the attenuation performance within the pass bands of conventional periodic structures and allows for easy adjustment of the attenuated bands without the need for physical structural modification. To characterize this system, a semi-analytical model of the electromechanical problem is developed using the Rayleigh–Ritz method, and the complex dispersion curve is obtained to evaluate the mitigation performance. The obtained results are validated against Finite Element Method (FEM) simulations, demonstrating that the lossy PZT-ABH metabeam achieves broadband vibration mitigation covering the entire frequency spectrum with remarkable flexibility. To facilitate designs, a detailed analysis is conducted on the length and attached position of the piezoelectric patch, thickness of the damping layer and the value of inductance and resistance. Furthermore, a thorough investigation into the mechanism of electromechanical resonance (ER) is carried out to deepen our understanding of the ER attenuated band.