  Periodic structures are a type of metamaterials in which their physical
properties not only depend on the unit cell materials but also the way unit
cells are arranged and interact with each other. Periodic structure have
Interesting wave propagation properties making them suitable materials for
acoustic filters and wave beaming devices. Bloch analysis is the main tool to
analyze wave propagation in these structures. In most if not all engineering
structures, each unit cell is interacting with adjacent cells. As such methods
developed for vibrational and wave propagation analysis of engineering periodic
structures, address forces exerted by the closest neighbor only. Since
metamaterials properties depend on the interactions of unit cell with
neighboring cells, more interactions means more complex band structure. In this
paper, we address force analysis when interactions are beyond the closest
neighbor. This analysis, lays the foundation for vibrational analysis of
structures in which interactions are not restricted to the closest neighbor.
