Applying nonlocal strain gradient theory to size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoplates

Abstract

In this research paper, as initial endeavors, the vibrational responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates taking into account the effect of nonlocal parameter and strain gradient coefficient are investigated. The study aims at developing mathematical modeling via an analytical solution to FG-CNTRC nanoplate structure with allowance for the nonlocal strain gradient effect. The four types of CNT distribution are used and compared in the context of the vibration of nanoplate in the presence of the small length scale effects, namely the (a) UD, (b) FG-V, (c) FG-O, and (d) FG-X. Some theoretical equations based on the first-order shear deformation plate theory (FSDT) are presented to provide a lucid understanding of how the small length-scale influences the FG-CNTRC nanoplate. For the vibrational analysis of a nanoplate, which is simply supported boundary condition, Navier solutions are obtained. Also, in contrast to earlier studies, an analytical approach is used to establish the governing equations of the FG-CNTRC nanoplate. Some specific numerical examples are given and compared with the results presented in the literature. In the section of numerical results, the influence of the nonlocal parameter, strain gradient coefficient, geometric parameters and vibrational modes on the non-dimensional natural frequency are investigated and discussed in detail. These could be useful to analysts and designers to estimate the fundamental natural frequencies in each of the four CNT distributions that the FG-CNTRC nanoplate possesses.