Uncertainty propagation in vibrational characteristics of functionally graded carbon nanotube-reinforced composite shell panels

Understanding the effect of mechanical uncertainties can play a significant role in design of the nanocomposites. The uncertain natural frequencies of moderately thick doubly-curved functionally graded composite panels reinforced by carbon nanotube (CNT) are investigated. Specifically, doubly-curved shell panels, including spherical, cylindrical and hyperbolic paraboloid panels are examined. To evaluate uncertainty propagation, uncertainty resources including distribution of the CNT through the thickness as well as the mechanical properties of the CNT and polymer matrix are taken into consideration. To assess the propagated uncertainties in the vibrational characteristics of nanocomposite panels, the interval analysis method is employed while the mechanical properties of nanocomposite panels are predicted using the modified rule of mixture method. Based on the comparison between the results of the present study and those reported in the literature, the accuracy of the results is validated. The sensitivity analysis is performed to distinguish the most prominent uncertain variables. Furthermore, numerical results reveal the influences of various uncertainty resources on the upper and lower bounds of uncertain frequencies and uncertainty propagation percent.