Continuum model of acoustic metamaterials with diatomic crystal lattice

ABSTRACT

The continuum model of one-dimensional acoustic metamaterial with diatomic crystal lattice is studied in this article. First, the dispersive relation of lattice wave in one-dimensional diatomic crystal lattice of metamaterial is established and compared with that of the classic material. Then, the continuum model of the acoustic metamaterial leads to the classical continuum model, the stain gradient continuum model, and the nonlocal gradient continuum model based on different assumptions. The dispersive curves, which correspond to the three kinds of models, are shown graphically and compared with that of discrete crystal lattice of metamaterial. The disadvantage of the classic continuum model and the strain gradient continuum model are discussed. The nonlocal gradient continuum model is derived based on the nonlocal assumption of continuous displacement field. The stability of dispersive curves is guaranteed. However, the actual prediction effects are still dependent upon the appropriate selection of the nonlocal parameter in the nonlocal gradient continuum model.

KEYWORDS:

• Metamaterial
• dispersion relations
• diatomic lattice
• strain gradient continuum
• nonlocal gradient continuum

Funding

The work is supported by the National Natural Science Foundation of China (No. 10972029) and Opening fund of State Key Laboratory of Nonlinear Mechanics (LNM).