Impact of non-linear resonators in periodic structures using a perturbation approach

The work describes the wave propagation in a periodic structure formed by a linear spring-mass chain with local Duffing non-linear resonators. The wave propagation of the system is studied using the Floquet-Bloch theorem combined with a perturbation approach to identify the dispersion relations in the nonlinear periodic structure. The theoretical model is benchmarked by a numerical approach based on imposing a wave number on a finite resonant spring-mass system as an initial condition, and then obtaining the corresponding frequency from the chain amplitude in the time domain. The perturbation and the numerical methods are compared to discuss the behaviour of the wave propagation in the nonlinear resonators periodic chain considered in this work The results from the perturbation techniques are also compared with the ones generated through an Harmonic Balance Method previously used in open literature. (C) 2019 Published by Elsevier Ltd.