Propagation of uncertainty in free vibration of graphene sheet rested on elastic foundation

Abstract

In this study, a convex model method is used to predict the uncertainty propagation in frequencies of graphene sheets rested on elastic foundation, resulting from the unavoidable scatter in parameters. The nonlocal plate model is utilised to include nanoscale size-effects, and an expression for the natural frequencies is proposed in an explicit form. The predicted results for the nominal case are compared with those obtained from molecular dynamic simulations. Uncertainty analysis of vibrational frequencies of the graphene sheets by using a non-probabilistic method is the main novelty of the present study. By using this method, the lower and upper bounds of the natural frequencies are evaluated. Numerical results indicate that the uncertainties must be considered for designing nanodevices.