The correlation between graphene characteristic parameters and resonant frequencies by Monte Carlo based stochastic finite element model

The uncertainty and fluctuations in graphene characteristic parameters are inevitable issues in both of experimental measurements and numerical investigations. In this paper, the correlations between characteristic parameters (Young’s modulus, Poisson’s ratio and thickness of graphene) and resonant frequencies are analyzed by the Monte Carlo based stochastic finite element model. Based on the Monte Carlo stochastic sampling procedure, the uncertainty in the characteristic parameters are properly propagated and quantified. The displacements and rotation modes of graphene under the resonant vibration computed by the finite element method are verified. Furthermore, the result robustness of stochastic samples is discussed based on the statistic records and probability density distributions. In addition, both the Pearson and Spearman correlation coefficients of the corresponding characteristic parameters are calculated and compared. The work in this paper provides a feasible and highly efficient method for the characteristic parameter correlation discussion by taking uncertainty into consideration.