Stochastic wave finite element quadratic formulation for periodic media: 1D and 2D. (February 2020) - Singh, R.P.; Droz, C.; Ichchou, M.; Franco, F.; Bareille, O.; De Rosa, S.
Graphical abstract: Video Abstract Highlights: A stochastic quadratic eigenvalue formulation for the periodic media is presented. The longitudinal and flexural waves in the 1D and 2D periodic media are simulated. In the case of flexural wave, only out of plane flexural wave are generated. The formulation offers huge computational advantages over the Monte Carlo simulation. Abstract: Periodic structures have properties of controlling mechanical waves. These solutions are used in aircraft, trains, submarines, space structures, where high level of robustness has to be ensured in presence of uncertainty in the numerical models. The paper presents a stochastic formulation for the Bloch analysis of periodic structures, based on the quadratic 1D and 2D forms of the Wave Finite Element method. In 1D case, numerical examples of periodic rod and metamaterial rod systems are considered; for the 2D case, homogeneous and periodic plates are considered. In both cases, the effect of uncertainties on wavenumber variation is studied. The accuracy and performance of the developed method is compared with Monte Carlo Simulation (MCS) results. It is found that the uncertainties affects the wavenumber scattering. Maximum variation of wavenumber occurs at the band gap edge frequencies and trends are increasing in higher frequency. In terms of computational cost, the presented formulation offers advantages over MCS. The obtained computational cost savings can be a remarkable achievement for the optimization and reliability study under uncertainties of complex structures.