  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
interesting property of such structures is that the band structures of such
metamaterials can be tuned by changing electric voltages.
