Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory

Abstract

This paper investigates the buckling and free vibration analysis of functionally graded carbon nanotube-reinforced composite thick rectangular nanoplates resting on a Kerr foundation under different boundary conditions. Quasi-three-dimensional hyperbolic shear deformation theory is employed to study the effects of transverse shear deformation and thickness stretching. To capture the small-size effects of nanoscale dimensions, the nonlocal strain gradient theory is used, which includes nonlocal parameters and length scale of the material. In this study, rectangular nanocomposite plates are reinforced by carbon nanotubes which are assumed to be graded through the thickness direction with four types of distributions, namely, uniformly, FG-O, FG-V, and FG-X. The governing equations and boundary conditions are extracted within Hamilton’s principle. They are discretized and numerically solved by utilizing a generalized differential quadrature method. The critical buckling loads and natural frequencies are determined by solving the eigenvalue problem. The accuracy of present results is validated with those available in the literature. Also, the effect of various factors, such as aspect ratio, length-to-thickness ratio, in-plane loading factor, length scale parameter, nonlocal parameter, volume fraction and dispersion profile of carbon nanotubes, elastic foundation coefficients, and different boundary conditions, on the buckling behavior and free vibration of nanoplates is investigated.