Nonlinear nonlocal phononic crystals with roton-like behavior

Thanks to their extraordinary dynamic characteristics, nonlinear phononic crystals (PCs) have found invaluable academic and industrial significance, in recent years. The dependence of wave propagation properties in phononic structures on material and geometrical specifications has led to innovative approaches to design them for specific needs. Along with the ongoing efforts to design and analyze more effective PCs, in this paper, we investigate the roton-like behavior of PCs by introducing a nonlinear monoatomic chain with the third-neighbor interactions able to exhibit backward energy flow in the Brillouin zone. We study the amplitude-dependent roton-like behavior of such crystals in detail, here. Furthermore, we analyze the effects of amplitude and nonlinear coefficients on the dispersion diagrams and backscattering regions of the introduced chain. We then expand the study to the nonlinear two-dimensional lattices to investigate the roton-like behavior in such structures. The results reveal that the roton-like behavior can lead to extraordinary characteristics in PCs and including nonlinearity can provide an extra level of control over their behavior.

Automated summary

Thanks to their extraordinary dynamic characteristics, nonlinear phononic crystals (PCs) have found invaluable academic and industrial significance, in recent years. In this paper, we investigate the roton-like behavior of PCs by introducing a nonlinear monoatomic chain with the third-neighbor interactions able to exhibit backward energy flow in the Brillouin zone. The results reveal that the roton-like behavior can lead to extraordinary characteristics in PCs and including nonlinearity can provide an extra level of control over their behavior.