Abstract
An adaptive metamaterial beam with a couple of electromechanical resonators in each unit cell is proposed in this study to open Bragg bandgap or locally resonant bandgap for flexural wave attenuation in Euler–Bernoulli beams. The electromechanical resonator is composed of a piezoelectric layer with segmented electrodes and shunt circuits, which affect the dynamic equivalent stiffness. It is illustrated that there is only a Bragg bandgap when the circuits of the two adjacent resonators are approximate to a short circuit or open circuit, and the locally resonant bandgap will be generated in the pure inductance circuits when the resonant frequencies are different in general. The locally resonant bandgap can be broadened by adding more resonators into the unit cell with the resonant frequencies of the shunting circuits satisfying a proper ratio.
Highlights
One of the most pronounced challenges in elastic metamaterial development is the ability to tune their performance in an adaptive manner without requiring physical structural modifications. e piezoelectric shunting technique was originally proposed by Forward [11] and further investigated by Hagood and von Flotow [12]. ese electromechanical resonators have the benefit of significantly lower mass requirements than purely mechanical massspring resonators. e use of piezoelectric elements shunted to resonating circuits has lately been explored for locally resonant bandgap formation. ese structures with resonating circuits can exhibit an electromechanical locally resonant bandgap
A couple of electromechanical resonators containing a piezoelectric layer with segmented electrodes and shunt circuit in one-unit cell are proposed to open Bragg bandgap or locally resonant bandgap for flexural wave attenuation in Euler–Bernoulli beams. Band structures in both pure resistance and inductance circuits have been studied by using the transfer matrix method and the discretization method will be applied as numerical validation. e effects of the circuit parameters, connections, and length ratio on the band structures of this electromechanical metamaterial beam are investigated. e analytical and numerical results demonstrate that a couple of electromechanical resonators in each unit cell is practicable to open Bragg bandgap or locally resonant bandgap
In analogy with the mechanical metamaterial, electromechanical metamaterial made from elastic substrates with piezoelectric layers shunted to shunting circuits exhibits bandgaps
Summary
E symbols l1 and l2 represent the length of subcell 1 and subcell 2, respectively, hs and hp are the thicknesses of the host beam and piezoelectric layers, and vj, vj2 and Yj1, Yj2 are the voltage and the external load admittance across the two subcells of the jth electrode pair. Where w(x, t) is the transverse displacement of the beam at position x and time t and vj and Yj1 are, respectively, the voltage and the external load admittance across the subcell 1 of the jth electrode pair. EI and m are the short-circuit flexural rigidity and mass per length of the beam motioned in equation (1), θ is the term associated with electromechanical coupling coefficient, and Cp, j1 and Cp, j2 are the internal piezoelectric capacitance across the subcell 1 and subcell 2 of jth electrode pair, given by. Equations (25) and (36) will be used
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