Stochastic wave finite element quadratic formulation for periodic media: 1D and 2D

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.