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

Abstract

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 nearfield 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 selfadaptive bandwidth in the far field. Our work will promote future studies, constructions and applications of NAMs with novel properties.

A brief review of metamaterials for opening low-frequency band gaps

“…Aimed at this issue, a nonlinear metamaterial is devised by replacing the linear springs in the resonator as nonlinear ones. The results show that resonant peaks in the frequency range between two band gaps are attenuated obviously owing to the bridging coupling effect [26,[112][113][114][115][116] . Such a frequency range is called the chaotic band gap, which provides a promising way to suppress the wave propagation in a much larger frequency range.…”

Rayleigh wave propagation in nonlinear metasurfaces

“…Although nonlinearity has been utilized to expand the available design space in metamaterials [1,26], its application in metasurfaces remains rare [3,27,28]. The most relevant studies, to the best of our knowledge, are those that involve nonlinear resonators attached to a one-dimensional substrate [29][30][31][32][33].…”

“…5. See [31] for a detailed example of third-harmonic generation in a similar problem in which the substrate is a thin beam.…”

Harmonic and shock wave propagation in bistable periodic structure: Regularity, randomness, and tunability

“…However, most research studies in this field are focusing on linear periodic structures based on the linear elastic mechanics. Many common laws have been revealed (Tang et al, 2019), including local resonances (Fang et al, 2018a, 2018b; Fossata et al, 2017), band gaps (Shahid et al, 2019), and defect states (Chou Chau et al, 2020; Thota and Wang, 2018).…”