Abstract
This study presents higher-order multiple scales analysis aimed at revealing angle- and amplitude-dependent invariant waveforms, and plane-wave stability, in two-dimensional periodic media. Multi-harmonic invariant waves arise from successive orders of particular solutions appearing in the multiple scales analysis. Simulations of nonlinear shear lattices confirm that inclusion of higher-order terms in the injected waveforms significantly reduce the ensuing growth of higher harmonics. These simulations also confirm the predicted directional-dependence of harmonic coefficients. In addition, the study assesses plane-wave stability using a local fixed-point analysis applied to the evolution equations, revealing angle-dependence in the stability characteristics. Based on the directional dependence uncovered, the study concludes with implications for encryption strategies and damage detection using weakly nonlinear lattices.
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