Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials
arXiv preprint arXiv:1812.05713, 2018•arxiv.org
In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is
investigated via the method of multiple scales. Commonly employed to the investigate the
effect of weakly nonlinear interactions on the free wave propagation through a phononic
structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is
here used to investigate the forced wave propagation through locally resonant
metamaterials. The perturbation approach reveals that energy exchange may occur …
investigated via the method of multiple scales. Commonly employed to the investigate the
effect of weakly nonlinear interactions on the free wave propagation through a phononic
structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is
here used to investigate the forced wave propagation through locally resonant
metamaterials. The perturbation approach reveals that energy exchange may occur …
In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction.
arxiv.org
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