Robustness Analysis of the Collective Dynamics of Nonlinear Periodic Structures Under Parametric Uncertainty

In order to ensure more realistic design of nonlinear periodic structures, the collective dynamics of a coupled pendulums system is investigated under parametric uncertainties. A generic discrete analytical model combining the multiple scales method, the perturbation theory and a standing-wave decomposition is proposed and adapted to the presence of uncertainties. These uncertainties are taken into account through a probabilistic modeling implying that the stochastic parameters vary according to random variables of chosen probability density functions. The proposed model leads to a set of coupled complex algebraic equations written according to the number and positions of the uncertainties in the structure and numerically solved using the time integration Runge-Kutta method. The uncertainty propagation through the established model is finally ensured using the Latin Hypercube Sampling method. The analysis of the dispersion, in term of variability of the frequency and amplitude intervals of the multistability domain shows the effects of uncertainties on the stability and nonlinearity of a three coupled pendulums structure. The nonlinear aspect is strengthened, the multistability domain is wider, more stable branches are obtained and thus the multimode solutions are enhanced.