Amplitude-induced acoustic bandgaps in cubically nonlinear metamaterials via nonlinear spring

In the present research, the wave-attenuation performance of a weakly nonlinear monoatomic metamaterial is controlled via a nonlinear auxiliary spring. More specifically, the “amplitudeinduced bandgaps”, which are exclusive to the nonlinear metamaterials and cannot be observed in linear metamaterials is scrutinized and impact of external control spring on such attenuation zones is analysed. A perturbation approach, based on the modified Lindstedt- Poincare method is used to analytically model the nonlinear monoatomic metamaterials and find the dispersion relations. It is found that the linear and nonlinear parts of the controlling spring have different effects on the wave propagation behavior of the 1-D metamaterial and while the linear part modulates the linear frequency, its cubic part can lead to changing amplitude- induced bandgaps. Additionally, carefully tuning the linear and nonlinear parts ofcontrolling spring, attenuation zones in desired parts of the frequency spectrum can be achieved. The results of the present article provide effective ethods in controlling the phononic characteristics of one-dimensional nonlinear metamaterials. Keywords: elastic metamaterial; bandgap; nonlinearity; phononic crystal.

Keywords:

elastic metamaterial , bandgap , nonlinearity , phononic crystal.