ABSTRACT
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.
ABSTRACT
This paper deals with a classical problem on a linear elastic lattice. A multi-mass-spring model is proposed to build the unit cell. Based on this multi-mass-spring model, a detailed investigation on the band of frequency gaps of one-dimensional periodic structures is conducted. A unified formulation to study the band structures of one-dimensional periodic structures is obtained. To determine the bound frequencies of the bands of frequency gaps, a very simple method without investigating the dispersion curves is proposed based on the modal analytical method. The method presented in this paper is applicable to general cases and is much more convenient than that proposed by other related investigations. In addition, the dynamic property of a finite periodic structure is investigated from the view of energy input, energy distribution, and interactions between the external excitation and the finite periodic structure, from which the energy flow pattern is illustrated clearly.
