Graded metamaterial with broadband active controllability for low-frequency vibration suppression

Abstract

This paper presents a new class of graded metamaterial beams by leveraging actively controllable resonators (ACR). The metamaterial comprises a homogeneous host beam that is mounted with negative capacitance shunted piezoelectric cantilever beams, each of which has a tip mass block. Properly changing the negative capacitances (NCs) in the stiffening/softening shunt circuits can control the formed bandgaps, providing greater adjustability and flexibility. Specifically, using modal analysis and considering higher modes of flexural vibrations, the ACR is simplified to an equivalent lumped parameter system with a correction factor applied to the reaction force. We demonstrate the relationship between the derived equivalent parameters of the ACR and NC for different circuitry configurations. A finite element model is built to validate the theoretical models of the ACR and the proposed metamaterial. Subsequently, a grading strategy is proposed to determine the NC values of ACR arrays for achieving broadband vibration suppression. A mechanical damping enhancement phenomenon that can contribute to forming an aggregated band is observed when resistances are introduced into the stiffening circuits. Three circuit configurations are examined, i.e., stiffening, softening, and hybrid circuits. The results showed that a proper grading coefficient can effectively suppress broadband vibration in the low-frequency range.