arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1808.04682physics.app-ph
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考虑三次谐波的无限大非线性声超材料梁中的波传播

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

Xin Fang, Jihong Wen, Dianlong Yu, Guoliang Huang, Jianfei Yin

摘要:

非线性声学超材料(NAM)开创了控制弹性波的新领域。在这项工作中,弯曲波传播的半无限NAM梁组成的周期Duffing谐振器的报告,考虑三次谐波产生(THG)。提出了不同的分析方法来描述波在等效均匀介质中的传播。通过与有限元法的比较,验证了该方法的有效性和准确性.我们揭示了分析和数值广泛的物理性质的强非线性AM,包括在一个细胞的非线性共振,有效密度,非线性局部共振(NLR)的带隙,传播和耦合的基波和三次谐波。这些特征是高度相关的,这有利于预测的功能。在近场,这些特征的相同的分叉频率作为基波的NLR带隙的起始频率,其宽度对于较强的非线性较窄。而在远场中,NLR带隙表征了导致自适应带宽的距离幅度依赖行为。此外,无限NAM的通带内的传输不同于有限NAM的混沌带效应,它受到移动的NLR间隙的影响。我们的工作将促进未来的研究和建设NAMs与新的性能。

英文摘要:

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.

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