Robustness Analysis of the Collective Nonlinear Dynamics of a Periodic Coupled Pendulums Chain

Perfect structural periodicity is disturbed in presence of imperfections. The present paper is based on a realistic modeling of imperfections, using uncertainties, to investigate the robustness of the collective nonlinear dynamics of a periodic coupled pendulums chain. A generic discrete analytical model combining multiple scales method and standing-wave decomposition is proposed. To propagate uncertainties through the established model, the generalized Polynomial Chaos Expansion is used and compared to the Latin Hypercube Sampling method. Effects of uncertainties are investigated on the stability and nonlinearity of two and three coupled pendulums chains. Results prove the satisfying approximation given by the generalized Polynomial Chaos Expansion for a significantly reduced computational time, with respect to the Latin Hypercube Sampling method. Dispersion analysis of the frequency responses show that the nonlinear aspect of the structure is strengthened, the multistability domain is wider, more stable branches are obtained and thus multimode solutions are enhanced. More fine analysis is allowed by the quantification of the variability of the attractors' contributions in the basins of attraction. Results demonstrate benefits of presence of imperfections in such periodic structure. In practice, imperfections can be functionalized to generate energy localization suitable for several engineering applications such as vibration energy harvesting.