Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

TL;DR

This paper applies the method of multiple scales to analyze how weak nonlinearities influence energy exchange between propagative and evanescent waves in 1D locally resonant metamaterials, revealing new interaction mechanisms.

Contribution

It introduces the use of the method of multiple scales for studying forced wave propagation in nonlinear locally resonant metamaterials, highlighting energy exchange phenomena.

Findings

Energy exchange occurs between propagative and evanescent waves due to quadratic nonlinear interactions.

The method reveals the influence of weak nonlinearities on wave dynamics in metamaterials.

The approach extends traditional analysis methods to complex nonlinear metamaterial behaviors.

Abstract

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.