On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

Abstract We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion obtain satisfactory accuracy when wavelength gets close spacing. Such applied displacement field lattice, resulting in novel SG model. For various kinds lattices, dispersion diagrams given by always agree well those discrete throughout first Brillouin zone, manifesting robustness present Based on this model, we conducted following discussions. (I) Both mass stiffness ratios affect band gap structures metamaterials, which very helpful for design metamaterials. (II) increase order can enhance performance if modified adopted. Without doing so, higher-order suffer from stronger instability issue does not necessarily better accuracy. eighth-order truncation found be enough capture behaviors all over zone. (III) effects interactions are analyzed. reduce workable range well-known long-wave approximation, causing more extrema diagrams. serve as theory spacing, i.e., approximation no longer valid. convenience designs, also provided space one easily proper corresponding requested width.