Broadening low-frequency bandgaps in locally resonant piezoelectric metamaterials by negative capacitance

This paper combines negative capacitance (NC) with inductance (L) to enlarge low-frequency bandgap width in locally resonant piezoelectric metamaterials. The studied metamaterials are obtained by directly bonding patches on the surfaces of host structures, then connecting patches to shunts. Shunts with NC and L in series and in parallel are both studied. Analytical expressions of the bandgap ranges are derived, which reveal that the bandgap size is increased not simply because the NC enhancing the material's electro-mechanical coupling factor, but in a more complicated way. Parametric studies are performed to analytically investigate the tuning properties of the LR bandgap by NC. Results demonstrate that by modifying NC value, the LR bandgap size can be significantly increased. Numerical simulations are done to verify the effects of the broadened bandgap on vibration transmission and reveal the limitations of the used analytical model. Practical implementation of the shunts are also discussed, recommendations on choosing the shunt configurations and NC values are given. This paper gives a theoretical guideline on designing piezoelectric metamaterials with bandgap effects at desired frequency ranges for practical applications like low-frequency vibration and noise reduction or isolation.