Wave propagation in infinite nonlinear acoustic metamaterial beam by considering the third harmonic generation

Nonlinear acoustic metamaterial (NAM) initiates new fields for controlling elastic waves. In this work, the flexural wave propagation in the half-infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation (THG). Different analytical methods are proposed to describe the wave propagation in the equivalent homogenous medium. Then their effectiveness and accuracy are demonstrated in comparison with the finite element methods. We unveil analytically and numerically extensive physical properties of the strongly nonlinear AM, including the nonlinear resonance in a cell, the effective density, nonlinear locally resonant (NLR) bandgap, propagations and couplings of the fundamental and the third harmonics. These characteristics are highly interrelated, which facilitates the prediction of functionalities. In the near field, the identical bifurcation frequency of these features acts as the start frequency of the NLR bandgap for fundamental waves, whose width is narrower for a stronger nonlinearity. While in the far field, the NLR bandgap characterizes a distance-amplitude-dependent behavior leading to a self-adaptive bandwidth. Moreover, the transmission in the passband of the infinite NAM is different from the chaotic band effect of finite NAMs, and it is influenced by the shifted NLR gap. Our work will promote future studies and constructions of NAMs with novel properties.