Periodic structure with electrostatic forces: Interactions beyond the nearest neighbor

Periodic structures are a type of metamaterial in which the physical properties depend not only on the details of the unit cell but also on how unit cells are arranged and interact with each other. In conventional engineering structures, each unit cell interacts with adjacent cells. Methods developed for vibrational and wave propagation analysis in periodic engineering structures consider only nearest-neighbor interactions. The dispersion curves of such systems, in which only adjacent cells interact, have been extensively studied. Metamaterial properties depend on the interactions of a unit cell with other cells. Further interactions, and specifically, interactions beyond the closest neighbors, imply a more complex band structure and wave behavior. In this paper, an example class of such structures, in which electrostatic forces are the driving force, has been investigated. In this paper, properties affecting these periodic structures, such as elastic forces, have been investigated. An attractive property of such structures is that the band structures of such metamaterials can be tuned by changing electric voltages.