Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation

Nonlinear acoustic metamaterials (NAMs) provide new ways to control elastic waves. In this work, flexural wave propagation in an infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation. Different analytical methods are proposed for the homogenized medium. By combining analytical and numerical approaches, we unveiled extensive physical properties of NAMs, including the nonlinear resonance, the effective density, the nonlinear locally resonant (NLR) bandgap, passbands, and the propagation and coupling of the fundamental and third harmonics. These characteristics are highly interrelated and they feature an identical near-field bifurcation frequency, which facilitates the prediction of functionalities. Moreover, we found that the NLR bandgap characterizes a distance-amplitude-dependent behavior that leads to a self-adaptive bandwidth in the far field. Our work will promote future studies, constructions and applications of NAMs with novel properties.