Dispersion Differences and Consistency of Artificial Periodic Structures

Dispersion differences and consistency of artificial periodic structures, including phononic crystals, elastic metamaterials, as well as periodic structures composited of phononic crystals and elastic metamaterials, are investigated in this paper. By developing a K(ω) method, complex dispersion relations and group/phase velocity curves of both the single-mechanism periodic structures and the mixing-mechanism periodic structures are calculated at first, from which dispersion differences of artificial periodic structures are discussed. Then, based on a unified formulation, dispersion consistency of artificial periodic structures is investigated. Through a comprehensive comparison study, the correctness for the unified formulation is verified. Mathematical derivations of the unified formulation for different artificial periodic structures are presented. Furthermore, physical meanings of the unified formulation are discussed in the energy-state space.