Vibration analysis of functionally graded carbon nanotube-reinforced composite nanoplates using Mindlin's strain gradient theory

In this paper, vibrations of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates are investigated. In doing so, the third order shear deformation theory is used and the size parameter is taken into consideration by using Mindlin's strain gradient theory. Equations of FG-CNTRC nanoplates motion with partial differentials are derived from Hamilton's principle. Mechanical properties of the FG-CNTRC nanoplates are determined using the rule of mixture. Here, the FG-CNTRC nanoplate is modeled as simply supported and the Navier solution is used to solve the vibration problem. The results of the new model are compared with those of the classical model, which leads to the conclusion that the classical model is a special case of the Mindlin's strain gradient theory. More results show that the rigidity of the FG-CNTRC nanoplates in the Mindlin's strain gradient theory is more than that in the classical theory, which leads to an increase in natural frequencies. Moreover, in the present study, the effect of the manner of distribution of Carbon nanotubes (CNTs) in the nanoplate and the effect of the volume fraction of the CNTs on the vibration of the FG-CNTRC nanoplates is investigated. (C) 2015 Elsevier Ltd. All rights reserved.