Free vibration analysis of polyethylene/CNT plates

.In this work, we analyzed the free vibration of single-walled carbon nanotubes (SWCNTs)-reinforced composite plates with carbon nanotubes (CNTs) embedded in amorphous polyethylene. Here, the governing differential equations of simply supported and clamped boundary conditions were found using the generalized differential quadrature (GDQ) method. We used the rules of mixture according to different plate models including first-order shear deformation theory (FSDT), classical plate theory (CLPT), and higher-order shear deformation theory (HSDT) to find the fundamental frequencies of nanocomposite plates. The properties of the materials used in the fabrication of nanocomposite plates were investigated using the Multiscale Finite Element Method (FEM) simulation for both short (10, 10) and long (10, 10) SWCNTs composites. The results of FEM simulations were fitted using those of the rule of mixture to obtain optimum values of CNT efficiency parameters. A few selected numerical results have been provided to investigate the effects of the volume fractions of CNTs and the types of edge supports on the value of fundamental frequency of long- and short-CNTs reinforced composite plates.