Metamaterial structures of beam or plate with periodic piezoelectric arrays have attracted more and more attention in recent years, which are conventionally designed for waveguide and/or wave propagation attenuation. The metamaterial structure with periodic piezoelectric shunts has also been explored for vibration control. R shunt and R-L shunt are traditionally adopted for the shunt circuit. An innovative type of high-order resonant circuit shunt is proposed and investigated for the periodic piezoelectric metamaterial in this paper. The introduction of an external inductor in the R-L shunt forms a resonance with the piezoelectric capacitance, which has the effect of reducing mechanical vibration at the resonant frequency of LC branch, with a certain bandwidth. The design of high-order resonant circuit shunt is introducing one more resonance around the resonant frequency, which is expected to broaden the bandwidth of the vibration attenuation. Finite element modeling of the metamaterial structure with periodic piezoelectric transducers is established. The method of obtaining the attenuation constant is also presented. Simulations have been conducted on comparing the vibration control performances among piezoelectric arrays with R shunt, R-L shunt, and the proposed high-order resonant circuit shunt. The simulation results illustrate that the proposed metamaterial structure with high-order resonant circuit shunts has broader vibration attenuation bandwidth. However, there is a tradeoff between the vibration attenuation amplitude and the vibration attenuation bandwidth, that is, although the high-order resonant circuit shunt has broader vibration reduction bandwidth, it cannot attenuate in larger amplitude.

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