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
|Number of pages||15|
|Journal||Mechanical Systems and Signal Processing|
|Early online date||10 Oct 2019|
|Publication status||Published - 1 Jan 2020|
- Periodic structures
Campana, M-A., Ouisse, M., Sadoulet-Reboul, E., Ruzzene, M., Neild, S. A., & Scarpa, F. (2020). Impact of non-linear resonators in periodic structures using a perturbation approach. Mechanical Systems and Signal Processing, 135, .