Analogue-twin interpretation of bandgap broadening in piezoelectric metamaterials

With the development of piezoelectric metamaterials, increasingly complex shunt circuits have improved tunability and broadband attenuation performance, but they also make repeated multiphysics simulations expensive and obscure how circuit design parameters govern attenuation-band evolution in finite structures. To address these issues, this study develops an impedance-based analogue-twin reduced-order model (AT-ROM) for a piezoelectric metamaterial beam with periodic patches shunted by parallel negative-capacitance (NC) and synthetic-inductance (SI) circuits. Based on the electromechanical analogy, the host-beam compliance, piezoelectric coupling, intrinsic blocked capacitance, NC and SI are condensed into a characteristic-branch impedance. Two anchor frequencies follow from this impedance: a zero that locates the low-impedance attenuation valley and a pole that bounds the negative-stiffness window, whose stiffness–weighted combination gives the bandgap edge of the actual cell. Their ratio is independent of the inductance, so the SI places the anchors on the frequency axis while the NC sets their separation, which yields an explicit two-parameter tuning rule and a nonlinear broadening trend of the bandgap. Unit-cell dispersion analysis, finite-element frequency-response comparison and experiments on a free–free steel beam with eight piezoelectric patches consistently confirm this behavior: the attenuation valley stays locked to the target mode while the attenuation band broadens with NC, and the model reproduces the finite-element response at about three orders of magnitude lower computational cost. This study provides a rapid and physically interpretable impedance-level bridge between shunt-circuit parameters and finite-structure attenuation-band evolution.