The influence of mechanical uncertainties on the free vibration of functionally graded graphene-reinforced porous nanocomposite shells of revolution

This paper is concerned with the analysis of uncertainty propagation in the free vibration response of functionally graded porous (FGP) nanocomposite shells of revolution reinforced with graphene platelet (GPL). In this regard, the effects of uncertainties in the material properties as well as the geometry of the reinforcements on the free vibration responses of the FGP-GPL shells with different types of Gaussian curvature are assessed. The propagation of uncertainty and frequency sensitivity of the shells of revolution are examined for various GPL dispersions and porosity distributions. For this purpose, the interval analysis method which is an appropriate technique for the uncertainty analysis of systems with bounded uncertainties is utilized. In order to solve the equations of motion based on the higher-order shear deformation theory and to obtain the free vibration responses of the shells of revolution, the Fourier Differential Quadrature (FDQ) technique is employed. According to the analysis results, the shells' type of curvature has a significant effect on the trend of uncertainty propagation and the sensitivity of the vibration frequencies in terms of various sources of uncertainty. Moreover, the results show that the uncertainty propagation and sensitivity are different in the frequencies corresponding to different modes of vibration.