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

Marc-Antoine Campana, Morvan Ouisse, Emeline Sadoulet-Reboul, M Ruzzene, Simon A Neild, Fabrizio Scarpa

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)
73 Downloads (Pure)


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 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 model that considers an analogous finite resonant spring-mass system. The numerical nonlinear model provides an apparent dispersion relation of the structure obtained from an inverse identification method, the latter based on imposing a wave number as an initial condition, and then obtaining the corresponding frequency from the analysis of 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. The perturbation is then compared with the Harmonic Balance Method previously used in the literature. Keywords: Periodic structures, Resonators, Non-linearities
Original languageEnglish
Article number106408
Number of pages15
JournalMechanical Systems and Signal Processing
Early online date10 Oct 2019
Publication statusPublished - 1 Jan 2020


  • Periodic structures
  • Resonators
  • Non-linearities


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