Uncertainty influence of nanofiller dispersibilities on the free vibration behavior of multi-layered functionally graded carbon nanotube-reinforced composite laminated plates

Uncertainties caused by the deviation of functionally graded reinforcements from the ideal linear distribution form are unavoidable during the manufacturing process, and this can significantly influence the vibrational behavior of carbon-based nanocomposite plates. In this context, this work aims to carry out a detailed parametric study on the free vibration response of laminated composite plates made of multi-layer carbon-based nanocomposite plies, considering both linear and nonlinear distribution forms of the nano-reinforcements. Materials constituting the plies are nano-reinforcement-based carbon nanotubes (CNTs) embedded in a polymer matrix. The CNTs are assumed to be either uniformly distributed (UD) or functionally graded (FG) across the ply thickness. Two types of laminated plate arrangements are comparatively investigated. The effective material properties such as elastic modulus and mass density are derived using the extended rule of mixture, whereas the governing equations are obtained through the combination of the Lagrange equation of motion and the first-order shear deformation theory (FSDT). The natural frequencies of the carbon nanotube-reinforced composite (CNTRC) laminated plates are obtained using the finite element method. The accuracy of the present numerical model is validated by comparing our results with those published in the open literature. The obtained numerical results show that both the plate layout arrangement and how the CNT fillers are dispersed along the ply thickness have a remarkable influence on the CNTRC laminated plates.