Nonlinear wave propagation in acoustic metamaterials with bilinear nonlinearity

Abstract

Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals. However, few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials. Hence, we introduce bilinear nonlinearity into acoustic metamaterials, and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method, revealing the influence of the system parameters. Furthermore, we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation, and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions. Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.