This article deals with the investigation of free vibration and buckling behaviors of carbon nanotube (CNT)-reinforced cross-ply laminated composite plates. The plate kinematics is assumed to follow a first-order shear deformation theory (FSDT). After the coupled equations of motion and buckling are derived, the method of discrete singular convolution (DSC) is used for the numerical solution of the problems. Both the regularized Shannon’s and Lagrange’s delta kernels are used for spatial discretizing of the resulting governing equations of buckling and vibration of CNT-reinforced laminated plates. Natural frequencies and critical buckling loads are obtained for different cases. Wherever possible, the present DSC results are verified by comparing them with the existing analytical results available in the literature. Then, a detailed parametric study is performed to examine the effects of boundary conditions, CNT distributions and volume fraction, aspect ratio, length-to-width ratio, and number of layers on the frequencies and buckling loads.

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

In this article, a highly efficient quasi-three-dimensional theory has been used to study the nonlinear hygro-thermo-mechanical bending analysis of a very thick functionally graded material (FGM) rotating disk in hygro-thermal environment considering the porosity as a structural defect. Two applied quasi-three-dimensional displacement fields are assumed in which the strain along the thickness ( ${\epsilon }_z$) is not zero unlike most of the other plate theories. By considering the nonlinear strains (von Kármán’s assumptions) the large deformations have also been taken into account in order to obtain more accurate results. Finally, some factors that affect the results have been studied further.