Roton-like dispersion and voltage enhancement in nonlocally resonant piezoelectric metamaterial beams

Abstract Roton-like dispersion, characterized by a maxon–roton pair on the lowest band, enables slow-wave and finite-wavenumber wave control, but is often realized through mechanically complex beyond-nearest-neighbor linkages. Here we demonstrate that roton-like dispersion can be achieved in a simple one-dimensional piezoelectric metamaterial beam using passive nonlocal electrical coupling. Periodically segmented bimorph electrodes are shunted by local inductors and additionally coupled to their N th-nearest neighbors via inductive connections, producing a wavenumber-dependent effective inductance and a dispersive electrical branch. Using a plane-wave expansion formulation for an infinite Euler–Bernoulli electromechanical lattice, we derive the Bloch eigenvalue problem and show that sufficiently strong third-nearest-neighbor coupling generates a pronounced maxon–roton feature in the lowest flexural branch. Finite-element simulations of a long chain of unit cells confirm the analytical dispersion predictions through frequency—wavenumber contours extracted by spatial Fourier analysis. Group-velocity results confirms a slow-wave region near the roton minimum, and spatial profiles show voltage amplification across many unit cells near this frequency. Finally, the voltage response of all unit cells reveals that appropriate separation between the local and nonlocal electrical resonant frequencies can substantially increase broadband voltage output